naive causality: a mental model theory of causal …modeltheory.org/papers/2001causality.pdfnaive...

Naive causality: a mental model theory of causal meaningand reasoning

Eugenia Goldvarga, P.N. Johnson-Lairdb,*aInfant Cognition Laboratory, Department of Brain and Cognitive Science, MIT, 77 Massachusetts Avenue,

Cambridge, MA 02139, USAbDepartment of Psychology, Princeton University, Green Hall, Princeton, NJ 08544, USA

All reasonings concerning matter of fact seem to be founded on the relation ofCause andEffect.

David Hume, 1748/1988

Abstract

This paper outlines a theory and computer implementation of causal meanings and reasoning. Themeanings depend on possibilities, and there are four weak causal relations:A causes B, A prevents B,A allows B,andA allows not-B,and two stronger relations of cause and prevention. Thus,A causesB corresponds to three possibilities: A and B, not-A and B, and not-A and not-B, with the temporalconstraint that B does not precede A; and the stronger relation conveys only the first and last of thesepossibilities. Individuals represent these relations in mental models of what is true in the variouspossibilities. The theory predicts a number of phenomena, and, contrary to many accounts, it impliesthat the meaning of causation is not probabilistic, differs from the meaning of enabling conditions, anddoes not depend on causal powers or mechanisms. The theory also implies that causal deductions donot depend on schemas or rules.

1. Introduction

You think about causal relations, because they allow you to infer what will happen.Drinking too much wine willcausea hangover. Spraying yourself with insect repellent willpreventmosquitoes from biting you. Taking a short cut willallow you to avoid the traffic.Reasoning about matters of fact is, as Hume says, largely based on causal relations.

* Corresponding author. Te.:11-609-258-4432; fax:11-609-258-1113.E-mail address:[email protected] (P.N. Johnson-Laird).

http://www.elsevier.com/locate/cogsciCognitive Science 25 (2001) 565–610

0364-0213/01/$ – see front matter © 2001 Cognitive Science Society, Inc. All rights reserved.PII: S0364-0213(01)00046-5

Psychologists have studied thinking about causal relations, but they have yet to agree on atheory of the process (see e.g., White, 1995; Ahn & Bailenson, 1996; Hilton & Erb, 1996;Cheng, 1997). Like philosophers, they also disagree about the meaning of causal claims. Ourconcern is not with the philosophical problems of causation – with whether causes reallyexist, with whether, if they do exist, they are objective states in the world or subjectivenotions in the mind, or with whether they hold between facts, events, processes, or states ofaffairs (cf. Vendler, 1967). Our aim is to develop a psychological account of causal meaningand reasoning. We assume that causes can concern events, processes, and also states ofaffairs, for example, for want of a nail the shoe was lost. And so we will use the neutralexpression, “states of affairs” or “states” for short, to embrace physical or psychologicalevents, situations, facts, and other potential arguments of causal relations. We have no doubtthat cause exists as an everyday concept, and we suspect that any sound philosophy ofcausation must reflect this fact. Otherwise, we pass over fine metaphysical distinctions, notbecause they are unimportant, but because they would take us too far afield from our maingoals.

Our concern is with the everyday causal claims and, in particular, with what naiveindividuals, that is, those who have not studied philosophy or logic, take such claims tomean. And our goals are to formulate a psychological theory of the semantics of causation,to examine its consequences, and to support it with corroboratory evidence. The theory offersan account of how people think about causality, and it purports to solve three puzzles: first,what causal relations mean; second, how they are mentally represented; and, third, howpeople make inferences from them. These questions are logically prior to the problem of theinduction of causal relations from observations. We need to knowwhat is induced before wecan properly understandhow it is induced. Our theory also has implications for severalcommon assumptions:

1. Causation is a probabilistic notion.2. There is no semantic or logical distinction between causes and enabling conditions.3. Inferences about causal relations depend on schemas or rules of inference.

If our theory is right, then each of these assumptions is wrong.The theory is based on mental models. They were originally postulated in order to explain

the comprehension of discourse (e.g., Stevenson, 1993; Garnham & Oakhill, 1996) anddeductive reasoning (e.g., Johnson-Laird & Byrne, 1991). Mental models are the end resultof perception, imagination, and the comprehension of discourse (Johnson-Laird, 1983). Eachmodel corresponds to a possibility, and models are labeled to distinguish physical, deontic,and logical possibilities (Johnson-Laird & Byrne, 1991). Causation depends on physicalpossibilities. Its counterparts in the other two domains are obligation and logical necessity.How people determine the status of a possibility–whether it is physical, deontic, or logical–isan important epistemological problem. It need not detain us, however, since the crucial factfor us is merely that they do make these distinctions.

The structure and content of a model capture what is common to the different ways inwhich the possibility can occur. According to the theory, naive reasoners imagine the statesof affairs described by premises: they construct mental models of them, and they establishthe validity of an inference by checking whether its conclusion holds in these models

566 E. Goldvarg, P.N. Johnson-Laird / Cognitive Science 25 (2001) 565–610

(Johnson-Laird & Byrne, 1991). The model theory offers a unified account of various sortsof reasoning. Thus, a conclusion is necessary–itmustbe the case–if it holds in all the modelsof the premises; it is possible–itmaybe the case–if it holds in at least one of the models; andits probability–assuming that each model is equiprobable–depends on the proportion ofmodels in which it holds. However, in order to minimize the load on working memory,people represent as little information as possible. A fundamental twofold assumption is:

The principle oftruth: i. The mental models of a set of assertions represent only thosesituations that are possible given the truth of the assertions. ii. Each such model representswhat is described by clauses in the premises (affirmative or negative) only when they are truewithin the possibility.

The principle is subtle, and so we illustrate how it works with an example. An exclusivedisjunction: There is a circle or else there is not a cross, calls for two mental models, one foreach possibility, which we represent on separate lines:

o

¬1

In accordance with the principle of truth, the first of these models represents explicitly thatthere is a circle, but it does not represent that in this possibility it is false that there is not across. Likewise, the second model represents explicitly that there is not a cross (“¬” denotesnegation), but it does not represent that in this possibility it is false that there is a circle. Thetheory assumes that reasoners try to remember what is false, but that these “mental footnotes”soon tend to be forgotten. If individuals can keep track of the mental footnotes, they canenvisagefully explicit models. Thus, the mental models of the preceding disjunction can befleshed out to yield the fully explicit models:

o 1

¬o ¬ 1

Do models never represent what is false? That cannot be the case, because an importantdevelopmental milestone is the ability to pass the “false beliefs” test. Thus, four-year olds areusually able to distinguish their own beliefs from the false beliefs of another individual (seee.g., Leslie, 1994). Children are likewise able to engage in pretense, to detect lies anddeception, and to reason on the basis of counterfactual suppositions. They may even be ableto carry out Wason’s (1966) selection task. In all these cases, as Denise Cummins (personalcommunication) pointed out, reasoners need to represent what is false. A crucial feature offalse beliefs in studies of the “theory of mind” is that they do not depend on sententialconnectives, that is, they are simple “atomic” beliefs (Alan Leslie, personal communication).It is straightforward to represent the falsity of such propositions, but it is much harder toenvisage what corresponds to the falsity of an assertion containing several sentential con-nectives. Even adults do not have direct access to these possibilities but must infer them (seeJohnson-Laird & Barres, 1994).

Experimental evidence has corroborated the model theory (see e.g., Johnson-Laird &Byrne, 1991). It accounts for reasoning about possibilities (Bell & Johnson-Laird, 1998),spatial and temporal relations (Byrne & Johnson-Laird, 1989; Schaeken et al., 1996);

567E. Goldvarg, P.N. Johnson-Laird / Cognitive Science 25 (2001) 565–610

counterfactual states (Byrne, 1997; McEleney & Byrne, 2001), probabilities (Johnson-Lairdet al., 1999), and the consistency of assertions (Johnson-Laird et al., 2000). Perhaps the bestevidence for the theory derives from its prediction of egregious, but systematic, errors (seee.g., Johnson-Laird & Savary, 1999; Yang & Johnson-Laird, 2000). We return to these“illusory” inferences in Section 4.

To explain tasks going beyond deduction, we must make additional assumptions. In thepresent paper, we frame a new theory based on assumptions about causation. The paperbegins with this theory and its computer implementation (Section 2). It reports studies ofcausal meanings that corroborate the theory (Section 3); and it reports studies of causal deductionthat also support it (Section 4). Finally, it considers some implications of the theory andshows how they dispel several common misconceptions about causation (Section 5).

2. The model theory of causal meanings and reasoning

Our aim is to outline a theory of the meaning of causal relations in everyday life and ofhow people reason with them. It is important, however, to distinguish three sorts of assertion:Generalcausal assertions such as:

Heating pieces of metal causes them to expand;Singularcausal assertions where the outcome is known, such as:

Heating this piece of metal caused it to expand;andSingularcausal assertions where the outcome is not known, such as:

Heating this piece of metal will cause it to expand.Hume (1748/1988, p. 115) bequeathed us two definitions of the meaning of causal assertions:“We may define a cause to bean object followed by another, and where all the objects,similar to the first, are followed by objects similar to the second.Or in other words,where,if the first object had not been, the second never had existed.” According to his firstdefinition, the general causal assertion above has the following construal: For any x, if x isa piece of metal and x is heated then x expands. Similarly, a singular cause where theoutcome is not known has the construal: If this piece of metal is heated then it will expand.According to Hume’s second definition, a singular cause where the outcome is known has acounterfactual construal: If this piece of metal had not been heated then it would not haveexpanded.

This section begins with the model theory of causal assertions, and contrasts it with othercurrent theories, including probabilistic accounts and theories that do not distinguish themeanings of causes and enabling conditions. It outlines the difference between mentalmodels and fully explicit models of causal relations. It describes a computer programimplementing the theory. It shows how causal reasoning can be based on models. Finally, itreviews the principal predictions of the theory.

2.1. The theory of meaning

There are at least five putative components of causation: temporal order, spatial contigu-ity, necessary connection, probabilistic connection, and causal powers or mechanisms.


Philosophers have long discussed these components (e.g., Hume, 1739/1978; Carnap, 1966;Lewis, 1973; and Mackie, 1980), and we consider each of them in order to develop the modeltheory.

2.1.1. Temporal orderIn daily life, the normal constraint on a causal relation between A and B is that B does not

precede A in time (see e.g., Tversky & Kahneman, 1980; Bullock et al., 1982). Hence, themodel theory postulates:

The principle oftemporal constraint:given two states of affairs, A and B, if A has a causalinfluence on B, then B does not precede A in time.

This principle allows that a cause can be contemporaneous with its effect–squeezing thetoothpaste tube, as Paolo Legrenzi noted (personal communication), can be contemporaneouswith the toothpaste coming out of the tube (see Kant, 1781/1934; Taylor, 1966). Teleologicalclaims–the need to get toothpaste caused the squeezing of the tube–do not violate theprinciple granted that a representation of the goal caused the behavior (Daniel Schwartz,personal communication). Hume (1739/1978) argued that the cause precedes the effect, andrejected contemporaneity. He finally declared that the matter was of no great importance. Acausal interpretation of Newton’s theory of gravitation, however, calls for instantaneouseffects at a distance. And individuals violate even our weaker constraint when in discussingtime travel, they assert that an event in the present caused an event in the past. Physicists andphilosophers have likewise speculated about violations of the temporal constraint. For thisreason, we treat it as true for everyday causal assertions, but as deliberately violated incertain sorts of discourse.

2.1.2. Spatial contiguityThere may be innate constraints on the perception of causal relations as when you see one

object bump into another and cause it to move (Michotte, 1946/1963). This claim iscorroborated by studies of infants’ perception (e.g., Leslie, 1984). It has led Geminiani et al.(1996), echoing Hume (1739/1978), to argue that adult conceptions of physical causationdepend ultimately on physical contact. Likewise, Lewis (1986) showed that three principlessuffice for a computer program that constructs models of a physical system: every event hasa cause; causes precede their effects; and an action on an object is likely to be the cause ofany change in it. Yet, the concept of causation in daily life is much broader and more abstractthan the perception of cause in simple Michotte-like mechanical events (Miller & Johnson-Laird, 1976). People often make and understand causal assertions that violate the constraintof spatial contiguity. They may refer to “action at a distance” in remarks about physicalstates, such as: The moon causes the tides, and in statements about psychological states: Pat’srudeness caused Viv to get annoyed. We accordingly assume that spatial contiguity–physicalcontact–is not a necessary component of the everydaymeaningof causal relations. But, itmay underlie many of the inferences that individuals make to explain such claims.

2.1.3. Necessary connectionAccording to the model theory, the central components of the meanings of causal relations

are the possibilities to which the relations refer:


Themodalprinciple of causation: given two states of affairs, A and B, the meaning of acausal relation between them concerns what is possible and what is impossible in theirco-occurrences (i.e., “modalities”).

This principle implies a necessary connection between cause and effect. Hume rejected sucha connection in favor of constant conjunction; Kant (1781/1934) restored it, arguing in effectthat it was a component of an innate conception. In everyday life, when we assertA willcause B,we mean that if A occurs then B must occur. Hence, necessity is part of the meaningof such claims (see Harre´ & Madden, 1975).

Following the principle of causal modalities, a singular causal claim of the formA willcause Bmeans that there are the following possibilities satisfying the temporal constraint:

1. a b

¬a b

¬ ¬b

Each row denotes a model of an alternative possibility. Thus, the models represent thepossibility of A with B, and possibilities in which A does not occur, either with or withoutB. The assertion is false if A occurs without B. A general causal claim,A causes B,calls forjust a single model of various possible events within the same situation or “universe ofdiscourse”:

a b

¬a b

¬a ¬b

¬a ¬b

Each row represents a possibility, and the various possibilities may co-occur in the situation.The assertion is false if there is a possibility in which A occurs without B. A singular causalassertion where the outcome is known,A caused B,has a model of the factual situation, andmodels representing alternative, but counterfactual, possibilities:

a b (the factual case)

¬a b (a counterfactual possibility)

¬a ¬b (a counterfactual possibility)

A counterfactual possibility is a state that was once was a real possibility but that did not, infact, occur (Johnson-Laird & Byrne, 1991). The falsity ofA caused Bis slightly morecomplicated than the previous cases. It is false, of course, if either A or B did not occur. But,it can be false even if both A and B occurred, because the relation between them was notcausal. Here the counterfactual possibilities are critical. If they include a case in which Aoccurred without B, or in which A occurred after B, then the assertion is false. These factualand counterfactual representations are consistent with Cheng’s (1997) concept of a “focal”set.


There are a variety of other causal relations, and each of them can occur in general andsingular assertions. For simplicity, we focus on singular causal relations with unknownoutcomes, and we take for granted the temporal constraint. An assertion of the formA willprevent Bmeans that there are the following possibilities:

2. a ¬b

¬a b

¬a ¬bIf the assertion is false, then there is a possibility in which A occurs with B.

An assertion of the formA will allow B such as: Taking the short cut will allow you toavoid the traffic, has a strongimplicaturethat not taking the short cut will not allow you toavoid the traffic. An implicature is an inference that is warranted by pragmatic considerations(see Grice, 1975; and for an account of how pragmatics is implemented within the modeltheory, see Johnson-Laird & Byrne, 2001). In this case, individuals who speak in aninformative way would not make the claim if they knew that one could just as well avoid thetraffic by not taking the short cut. Thus, an assertion of the formA will allow B means eitherthat all four contingencies are possible or that there are the following three possibilitiessatisfying the implicature:

3. a b

a ¬b

¬a ¬bThe assertion is false if there is a possibility in which B occurs in the absence of A. The verballow is ambiguous in that it also has a sense of giving permission. Some authors accordinglyprefer to use the verbenableand to talk of “enabling conditions.” Unfortunately, this verbtoo can have the same ambiguity (cf. “The Royal toast enabled us to smoke”). In fact, theambiguity appears to arise from the fact that both senses can be construed asto makepossible,where in one case the possibility concerns physical matters and in the other case itconcerns deontic matters, that is, what is permissible. In general, we will use “allow” because“enable” has a connotation that the result was intended. It is odd to assert, for example:Shoddy work enabled the house to collapse.

An assertion of the formA will allow not B means either that all four contingencies arepossible or that there are the following three possibilities satisfying the implicature:4. a ¬b

a b

¬a bIt is sometimes important to distinguish between meaning and implicature, but in whatfollows we will not attempt to keep them apart.

The preceding relations are weak, for example, givenA will cause B,A is sufficient forB, but not necessary, because B may have other causes. Indeed, if one ignores the temporalconstraint, the models of causal possibilities capture the notion ofsufficiencyand the modelsof enabling possibilities capture the notion ofnecessityas invoked by various theorists (e.g.,


Thompson, 1995). An example of weak causation is: Eating too much will cause you to gainweight. You may also gain weight as a result of failing to exercise. In addition to the fourweak relations, there are two strong relations.A, and only A, will cause Bmeans that thereare the following possibilities satisfying the temporal constraint:

5. a b

¬a ¬b

In other words, A is the unique cause and enabler of B. AndA, and only A, will prevent Bmeans that there are the following possibilities satisfying the temporal constraint:

6. a ¬b

¬a b

A case of strong causation is: Drinking too much alcohol will cause you to get drunk.Drunkenness has no other cause. The models for the six causal relations are summarized inTable 2 below.

There is no causal relation if A or B is bound to occur or bound not to occur; and Cheng& Nisbett (1993) have shown that naive individuals concur with this claim. An assertion suchas: “The rotation of the earth causes the prevailing wind patterns,” might seem like acounterexample on the grounds that the earth is bound to move. In fact, naı¨ve individualsreadily envisage the counterfactual possibility that the earth does not rotate, because theyassent to the claim: If the earth were not to rotate then there might be no prevailing windpatterns. If all you know is that B is bound to occur if A occurs, then you are not entitled tomake any causal claim about the relation between them. On the one hand, B may also bebound to occur even if A does not occur, that is, there are only the following possibilities:

a b

¬a b

and so it would be wrong to invoke a causal relation between A and B. On the other hand,even granted a causal relation between the two, A could be a strong or a weak cause of B.The existence of several sorts of causal relation may come as a surprise to the reader.Philosophers have often seemed to assume that there is only a single relation of cause andeffect, and, according to Lombard (1990), their neglect of enabling conditions has led theminto error.

The general weak relations depend on the temporal constraint and quantification overpossible states, that is, the relations are not merely truth-functional:

1. A causes B: for any possibility in which A occurs B occurs.2. A prevents B: for any possibility in which A occurs B does not occur.3. A allows B: there is at least one possibility in which A occurs and B occurs.4. A allows not B: there is at least one possibility in which A occurs and B does not occur.

The assertion: For any possibility in which A occurs B occurs, is logically equivalent to:There is no possibility in which A occurs and B does not occur. Of course, individuals oftenassert general causal claims, such as: Smoking causes cancer, when they know that coun-


terexamples occur. This phenomenon has led some theorists to invoke a probabilisticanalysis of causation–an analysis that we consider below.

Our account implies that there should be many ways to describe causal relations. Thisvariety has advantages. Three possibilities are hard to hold in mind at the same time, but onedescription can focus on one possibility and another description focus on another possibility:

1. a b A causes B

¬a b

¬a ¬b Not-A allows not-B

2. a ¬b A prevents B

¬a b Not-A allows B

¬a ¬b

3. a b A allows B

a ¬b

¬a ¬b Not-A prevents B

4. a b

a ¬b A allows not-B

¬a b Not-A causes B

The same analysis applies to the large set of verbs that express specific causal relations, suchasannoy, kill,andbreak (see Miller & Johnson-Laird, 1976, Sec. 6.3).

2.1.4. Probabilistic connectionIn contrast to the model theory’s modal account, a twentieth century view in philosophy

and psychology is that causation is a probabilistic notion. Reichenbach (1956) proposed suchan analysis, arguing thatC causes Eif:

p(EC) . p(E¬C)

where p(EC) denotes the conditional probability of the effect E given that the putative causeC occurs, and p(E¬ C) denotes the probability of the effect given that the cause doesnotoccur. He allowed, however, that a putative cause could be “screened off” if there was anearlier probabilistic cause, D, yielding both C and E, that is, p(EC) 5 p (ED), and p (E¬C) 5 p (E¬ D). Suppes (1970) defended a similar analysis, even for causation in ordinaryexperience (see also Suppes, 1984, p. 54; and Salmon, e.g., 1980, for a defense of a moresophisticated theory).

A psychological theory of probabilistic causes has been defended by Cheng and hercolleagues (e.g., Cheng & Novick, 1990; see also Schustack, 1988). There are also parallelprobabilistic accounts of the meaning of conditionals (see e.g., Newstead et al., 1997).“Because causal relations are neither observable nor deducible,” Cheng (1997, p. 367) writes,“they must be induced from observable events.” She assumes that one observes the differ-


ence in the respective conditional probabilities shown in the inequality above. The proba-bilities can be computed from a partition of the events, such as the following one stated withfrequencies of occurrence:

C E 28

C ¬E 3

¬C E 10

¬C ¬E 59

The difference between p(E C) and p (E ¬ C) is known as the probabilisticcontrast.When it is noticeably positive (as above: 0.76),C causes E;when it is noticeably negative,C prevents E.The contrast model fails to make the correct predictions for certain causalinductions, and so Cheng (1997) has proposed a “power probabilistic contrast” model (thePower PC model) in which the contrast is normalized by dividing it by the base rate for theeffect, that is, 1 – P(E ¬ C).

The main evidence for a probabilistic semantics is that people judge that a causal relationholds in cases, such as the partition above, in which the antecedent is neither necessary norsufficient to bring about the effect (e.g., McArthur, 1972; Cheng & Novick, 1990; Cumminset al., 1991). One might therefore suppose that causal relations are intrinsically probabilistic.Certainly, people ofteninducecausal relations from probabilistic data. Yet, our hypothesisis that the meaning of a causal relation is not probabilistic, though the evidence supportingit may be probabilistic. We return to this hypothesis later in the light of our experimentalresults.

2.1.5. Causal powers or mechanismsTheorists often invoke some causal power, mechanism, or means of production, over and

above the relevant possibilities (e.g., Harre´ & Madden, 1975; Ahn et al., 1995; White, 1995;and Cheng, 1997). One candidate might be a framework of scientific laws or explanatoryprinciples (Carnap, 1966). These principles, Hart & Honore´ (1985) argue, lie behind everycausal assertion about singular events. Another candidate is that “a causal mechanism is theprocess by which a cause brings about an effect” (Koslowski, 1996, p. 6). Still anothercandidate is the notion that causes produce effects through a transmission of energy or someother property from cause to effect. “In this sense,” Harre´ & Madden (1975, p. 5) write,“causation always involves a material particular which produces or generates something.”When a hammer is used to smash a plate, for example, a specific causal power of the hammerblow produces the effect: the energy in the blow is transferred to the plate, causing it tobreak. Theories of causal power accordingly define causation in terms of the intrinsicproperties of objects. Hume (1739/1978), however, rejected intrinsic properties that produceeffects, arguing that the definition ofproductionis indistinguishable from that of causationitself.

The principal evidence for causal power comes from studies showing that beliefs canoverride information about the covariation of cause and effect (e.g., White, 1995; Koslowski,1996). The phenomena, however, do not call for the introduction of causal properties,


powers, or mechanisms, into themeaningof causal relations. People make causal assertionswhen they have no idea of the underlying causal mechanism, for example: Smoking opiumcauses people to fall asleep. Hence, the meaning of many assertions would imply at mostonly that some unknown power exists:A causes Bmeans that there exists a mechanism orpower by which A causes B. But, it would then be necessary for theorists to specify whatcounts as a causal mechanism or power, or else the existential clause in this analysis isvacuous. To the best of our knowledge, as Hume anticipated, no-one has succeeded informulating a satisfactory definition of a causal power or mechanism, which itself makes noreference to causality. Our skepticism, however, in no way impugns the role of known causalmechanisms in the induction of causal relations–a topic to which we return in the GeneralDiscussion.

2.2. Circumstances and how causes differ in meaning from enabling conditionsThe model theory distinguishes between causing an effect and allowing it to occur, that

is, between causes and enabling conditions. Yet, current psychological theories deny thatthere is any logical or semantic distinction between the two. The argument, which isoriginally due to Mill (1874), influenced philosophers and jurists first, and then psycholo-gists. It can be illustrated by an example of a singular cause. Consider an explosion that iscaused by the occurrence of a spark in a container of combustible vapor. The explosionwould not have occurred in the absence of the spark, and it would not have occurred in theabsence of the vapor. Hence, both the spark and the vapor are individually necessary andjointly sufficient to cause the explosion. Yet, people often speak of the spark as thecauseofthe explosion, and the presence of the vapor as theenablingcondition that allows it to occur.Likewise, the absence of the spark or the vapor would be adisablingcondition that wouldnot allow the explosion to occur (see Cummins, 1995, 1998). If the difference betweencauses and enabling conditions cannot be accounted for by logic or meaning, then whatdistinguishes the two? Mill himself thought that the choice of a cause was often capricious,but he did offer some more systematic answers, as have many other authors.

According to one school of thought, causes are abnormal whereas enabling conditions arenormal. Thus, Hart & Honore´ (1959/1985) argued that when individuals identify singlecauses, they choose the unusual factor as the cause–the spark rather than the vapor in theexample above, or else they choose a voluntary human action. Girotto et al., (1991) haveindependently discovered that voluntary human actions are the main events that reasonersseek to undo in thinking counterfactually about the causes of unfortunate events. Variousways exist to try to determine what is unusual. One can distinguish what is rare and what iscommon (Hart & Honore´, 1959/1985), what is inconstant and what is constant (Cheng &Novick, 1991), or what does and does not violate a norm that can be assumed by default (seee.g., Kahneman & Tversky, 1982; Kahneman & Miller, 1986; Einhorn & Hogarth, 1986).

According to another school of thought, the cause is the factor that is conversationallyrelevant in explanations (Mackie, 1980; Turnbull & Slugoski, 1988). Thus, Hilton & Erb(1996) argue for a two stage process: “explanations are first cognitively generated bybuilding mental models of the causal structure of events, from which particular factors areidentified in conversationally given explanations” (p. 275). These authors adduce Grice’s(1975) maxims of conversation as determining the cause, but they allow that other accounts


of pragmatics would serve as well. Yet another school of thought supposes that it is the mostrecent or precipitating event that is the cause (Mill, 1874), and there are still other views (seeHesslow, 1988, for a review). Table 1 summarizes the main hypotheses about the distinctionbetween causes and enabling conditions. Of course, all these components might be true, andyet we will show that thereis a difference in meaning too.

To recapitulate the argument: the model theory entails that a distinction in meaning andlogic exists between causing and allowing. Other psychological theories presuppose that thetwo are not logically distinct. Hence, an apparent paradox needs to be resolved. We need toexplain why Mill’s argument seems so compelling. In fact, the answer comes from the subtleeffects of knowledge in determining thecircumstancesof a cause and effect.

Suppose you observe the following sequence of events: A doctor injects a patient with adrug, and then the patient loses consciousness. What is the causal relation, if any, betweenthe two events? The observation is inconsistent with two causal relations: the injection didnot prevent loss of consciousness in either its strong or weak sense. But, it is compatible withany of the four remaining relations and, of course, with the lack of any causal relation at all.A corollary of this uncertainty is that the mere observation of a particular sequence ofstates–in the absence of knowledge about causal relations–never suffices to establish aunique causal relation. Even the simple perception of physical causes, as in Michotte’s(1963) studies, is not a counterexample. The participants saw a causal relation when oneobject collided with another and launched it into motion. They were mistaken of course,because Michotte’s apparatus did not use real physical objects colliding with one another.Causal relations are modal. They are not merely about what occurred but also about whatmight have occurred. What might have occurred, however, cannot be determined fromobservation unsupported by knowledge of the circumstances. The model theory accordinglypostulates:

The principle of circumstantial interpretation: Causal interpretation depends on howpeople conceive the circumstances of states, that is, on the particular states that theyconsider to be possible, whether real, hypothetical, or counterfactual.

Precursors to this idea include Hart & Honore´’s (1959/1985) and McGill’s (1989) “context”of a cause, Mackie’s (1980) “causal field,” and Cheng & Novick’s (1991) “focal set” ofevents. The circumstantial principle, however, implies that you use your general knowledge

Table 1A summary of hypotheses about the difference between causes and enabling conditions. All these accountspresuppose that there is no difference in meaning or logic between the two

Distinguishing characteristics Examples of proponents

Causes Enabling conditions

Most recent event Earlier event Mill (1874)Rare event Common event Hart and Honore´ (1985)Inconstant state Constant state Cheng and Novick (1991)Violates norm Conforms to norm Einhorn and Hogarth (1978)Relevant to conversation Not relevant Mackie (1980)

Turnbull and Slugoski (1988)Hilton and Erb (1996)


and your knowledge of the state at issue to generate models. In the case of a singular causalclaim, one model represents the actual state, and the other models represent the relevantpossibilities in the circumstances. The models fix the appropriate causal relation.

To return to the preceding example, if the circumstances are as follows:

injection loss-of-consciousness

¬injection loss-of-consciousness

¬injection ¬loss-of-consciousness

an appropriate description is: The injection caused the patient to lose consciousness. If thecircumstances are as follows:


injection ¬loss-of-consciousness


an appropriate description is: The injection allowed the patient to lose consciousness. And ifthe circumstances are as follows:


injection ¬loss-of-consciousness

¬injection loss-of-consciousness

an appropriate description is: The injection did not prevent the patient from losing con-sciousness.

The truth of an assertion about past states of affairs, such as: The injection caused thepatient to lose consciousness, presupposes that the patient had an injection and that thepatient lost consciousness. But, a causal relation is not true merely because both propositionsthat it interrelates are true (Burks, 1951; Mackie, 1980). Even granted the temporal constrainton the order of the two events, the modal nature of causation is borne out by its support forcounterfactual claims (see Hume, 1748/1988; Mill, 1874; and many recent accounts). Acorollary is that the appropriate description of an observation depends on circumstantialinterpretation. Consider the circumstances of a strong causal relation, such as:



With an observation corresponding to the first of these models, the appropriate counterfactualassertion is: If the patient hadn’t had the injection, then he wouldn’t have lost consciousness.With an observation corresponding to the second of the models, the appropriate counterfac-tual assertion is: If the patient had had the injection, then he would have lost consciousness.Counterfactual descriptions are not unique to singular causal claims, as an example fromLewis (1973) illustrates: If kangaroos had no tails then they would topple over, is just anotherway of expressing the general claim: Kangaroos’ tails prevent them from toppling over.


What are the correct circumstances of a state? Well, it all depends. Often, there are nodecisive criteria. That is why the circumstances–theceteris paribusclause of counterfactualconditionals–have bedeviled philosophical analyses (e.g., Stalnaker, 1968). They play animportant role in blocking otherwise valid inferences of the following sort (see e.g., Lewis,1973):

If the match had been struck, then it would have lighted.[ If the match had been soaked in water and struck, then it would have lighted.

The circumstances of the conclusion are no longer those of the premises. The case is altered;the conclusion is false even if the premise is true (see Johnson-Laird & Byrne, 2001, for anaccount of how general knowledge modulates the interpretation of such conditionals).

We can now consider again the example illustrating Mill’s argument. A spark in acombustible vapor causes an explosion. You know that in the presence of the vapor, the sparkcauses the explosion, and that in the absence of either the vapor or the spark, there is noexplosion. Your knowledge accordingly yields the circumstances shown in the followingmodels:

vapor spark explosion

vapor ¬spark ¬explosion

¬vapor spark ¬explosion

¬vapor ¬spark ¬explosion

The roles of the spark and vaporare equivalent. Jointly, they are the strong cause of theexplosion.

You can envisage other circumstances. Suppose, for example, that a tank is used tostore gasoline, and at present it may or may not contain a combustible vapor. Thepresence of the vapor will allow an explosion to occur, and the occurrence of a spark,or, say, a naked flame will cause an explosion. The circumstances are shown in thefollowing models:

vapor spark explosion

vapor ¬spark explosion

vapor ¬spark ¬explosion

¬vapor spark ¬explosion

¬vapor ¬spark ¬explosion

The respective roles of the two antecedents are logically distinct. The possible combinationsof vapor and explosion in the set of models are as follows:

vapor explosion

vapor ¬explosion

¬vapor ¬explosion


They show that the vapor allows the explosion to occur. The possible combinations of sparkand explosion in the set of models are as follows:

spark explosion

spark ¬explosion

¬spark explosion

¬spark ¬explosion

The full set of circumstances, however, shows that given the presence of the vapor, the sparkcauses the explosion to occur.

You can envisage circumstances in which the causal roles of the vapor and spark areinterchanged. Suppose, for example, that an induction coil delivers a spark from time to timein an enclosed canister. You know that the introduction of a combustible vapor will cause anexplosion. You also know that the occurrence of the spark allows such an explosion to occur.It may even occur without the vapor if, say, an explosive substance such as gunpowder is putinto the canister. The circumstances are as follows:

spark vapor explosion

spark ¬vapor explosion

spark ¬vapor ¬explosion

¬spark vapor ¬explosion

¬spark ¬vapor ¬explosion

The spark allows the explosion to occur, and given its occurrence, the vapor causes theexplosion.

This analysis shows that causes and enabling conditions are distinct, and that theyreflect the modal and circumstantial principles. The respective probabilities of each ofthe possibilities can make one antecedent common and the other antecedent rare, but theprobabilities have no bearing on their causal roles (paceHart & Honore, 1959/1985).Indeed, the switch in causal roles from one set of circumstances to the other shows thatnone of the factors in Table 1 is essential to distinguishing between causes and enablingconditions. Causes need not be unusual or abnormal, and they need not be pragmaticallyrelevant to explanations. Cheng & Novick’s (1991) experiments corroborated both theseclaims, and their theory of causal induction also relies on sets of possibilities. But, theyargued that enabling conditions areconstantin a set of possibilities whereas causes arenot constant (see also Cheng, 1997). It is true that enabling conditions are constant insome circumstances. But, our preceding examples show that constancy in the circum-stances is not necessary for an enabling condition. Neither the spark nor the vapor isconstant in the circumstances above, yet their logical roles are distinct, and one is anenabling condition for the other to function as a cause.


2.3. Mental models of causal relations

Our preceding analysis of the meanings of causal relations is in terms of fully explicitmodels. The principle of truth, however, predicts that naive individuals will tend to rely onthe correspondingmentalmodels for each of the causal relations. An assertion of the form:A will cause B,calls for the mental models:

a b

. . .

in which the ellipsis represents implicitly possibilities in which the antecedent, A, does nothold. There is a mental footnote to capture this fact–in effect, A cannot occur in thepossibilities represented by the implicit model. Given the mental footnote, it is possible toflesh out the models fully explicitly as:

a b

¬a b

¬a ¬b

The theory postulates that individuals normally reason on the basis of mental models, butwith simple assertions of the present sort, they can appreciate thatA will cause B iscompatible with B having other causes. Given time, they may even enumerate all threeexplicit possibilities. Strong causation as expressed byA, and only A, will cause Bhas thesame mental models as weak causation, but the mental footnote indicates that neither A norB can occur in the possibilities represented by the implicit model, and so the only way toflesh out the model fully explicitly is as shown below:

a b

¬a ¬b

An assertion of the form:A will prevent B,relies on a negative verb (Clark & Clark, 1977),and so it means that if A occurs then B does not occur in the circumstances:

a ¬b

. . .

where there is a mental footnote indicating that A cannot occur in the possibilities repre-sented by the implicit model. Again, individuals may be able to enumerate the explicitpossibilities, but normally they should use mental models to think about the relation.Analogous considerations apply to assertions of the form:A allows B,andA allows not B.

2.4. The computational implementation of the theory

We have developed a computer program of the model theory. Its input is a set of causalassertions, and it constructs the corresponding set of mental models and, for purposes ofcomparison, the set of fully explicit models. It also draws the causal conclusion, if any, that


the resulting models support. The program uses a grammar to parse each input sentence, andit relies on a lexical semantics for causal verbs, and a compositional semantics with semanticrules for each rule in the grammar to assemble the models. The models for each of the sixsingular causal relations with unknown outcomes are summarized in Table 2. When theoutcome is known, the remaining models represent counterfactual states. The models in thetable also stand for general causal assertions, but in this case each row represents analternative possibility within the same situation.

The program conjoins sets of models according to the procedures summarized inTable 3. These procedures combine separate possibilities, either those corresponding tomodels of singular causal assertions or those in models of general causal assertions.Readers will recall that for general assertions, the theory postulates that reasoners construct asingle model representing the different sorts of possibilities. We make no strong claims thatreasoners form separate models and then combine them; they might instead add informationfrom a premise to an existing model or set of models (see e.g., Bucciarelli & Johnson-Laird,1999). In either case, however, the process yields the same end results.

Different sorts of model support different sorts of conclusions. In particular, the programuses a single model of the possibilities:

a c

. . .

to draw the general conclusion,A causes C.From a single model of the form:

Table 2The models for the six singular causal relations with unknown outcomes. The central column shows themental models normally used by human reasoners, and the right-hand column shows the fully explicitmodels, which represent the false components of the true cases using negations that are true: “¬” denotesnegation and “. . .” denotes a wholly implicit possibility. The mental models for the strong and weak relationsof cause and prevention differ only in their mental footnotes (see text).

Connective Mental models Fully Explicit models

1. A will cause B: A B A B. . . ¬A B

¬A ¬B

2. A will prevent B: A ¬B A ¬B. . . ¬A B

¬A ¬B

3. A will allow B: A B A B. . . A ¬B

¬A ¬B

4. A will allow not-B: A ¬B A ¬B. . . A B

¬A B

5. A and only A will cause B: A B A B. . . ¬A ¬B

6. A and only A will prevent B: A ¬B A ¬B. . . ¬A B


a c

a

. . .

it draws the conclusion,A allows C.The program draws negative conclusions from two sortsof models, which both must contain negative tokens, either of an end term or a middle term.The model:

a ¬c

. . .

and the model:

a

c

. . .

yield the conclusion,A prevents C.Likewise, the model:

a ¬c

a

. . .

and the model:

Table 3The procedures for forming a conjunction of two sets of possibilities. The procedures apply either toindividual models (based on singular causal relations) or to individual possibilities (based on general causalrelations). Each procedure is presented with an accompanying example. In principle, each procedure shouldtake into account mental footnotes, but reasoners soon forget them. The program implementing the theoryalso reasons at more advanced levels, first taking footnotes into account, and then constructing fullyexplicit models.

1. For a pair of explicit items, the result conjoins their elements, and drops any duplicates:a b and b c yield a b c

2. For a pair of items that contain an element and its contradiction, the result is null (akin to the empty set):a b and ¬b c yield null

3. For null combined with any item, the result is null:null and a b yield null

4. For a pair of implicit items, the result is implicit:. . . and . . . yield . . .

5. For an implicit item combined with an explicit one, the result by default is null:. . . and b c yield null

But, if the explicit item contains no element in common with anything in the same set from which theimplicit item is drawn, then the result is the explicit item:

. . . and b c yield b c


a c

a

. . .

yield the conclusion,A allows not-C.We illustrate how the program works by elucidating the contrast between causal forks and

causal chains. Fisher (1959) argued that smoking might not be a cause of lung cancer, andthat instead there could be an unknown gene, X, that both causes people to smoke andindependently causes them to get lung cancer. If they have the deadly gene then they arelikely to develop cancer whether or not they smoke. If they do not have the deadly gene thenthey are unlikely to develop cancer whether or not they smoke. Ergo, they might as wellsmoke. A contrasting view is that a causal chain occurs: the gene causes smoking, andsmoking causes cancer. Given the assertions for a causal fork:

Gene causes smoking.Gene causes cancer.

the program constructs the following fully explicit model:

Gene Smoking Cancer

¬Gene Smoking Cancer

¬Gene Smoking ¬Cancer

¬Gene ¬Smoking Cancer

¬Gene ¬Smoking ¬Cancer

The causal fork allows a possibility in which smoking occurs without cancer. In contrast,given the assertions for a chain of weak causes:

Gene causes smoking.Smoking causes cancer.

the program constructs the following set of fully explicit models:

Gene Smoking Cancer

¬Gene Smoking Cancer

¬Gene ¬Smoking Cancer

¬Gene ¬Smoking ¬Cancer

Both the gene and smoking cause cancer.

2.5. Deductive inferences from causal relations

Some theorists suppose that causes cannot be deduced, but only induced. But, the causalstatus of an observationcanbe deduced from knowledge of its circumstances. For example,suppose you know that a certain anesthetic causes a loss of consciousness, and you observethat a patient who is given the anesthetic loses consciousness. You can deduce that the


anestheticcausedthe patient to lose consciousness. How do you make such deductions?There are three potential answers.

The first answer is that you rely on formal rules of inference (see e.g., Braine & O’Brien,1998). One such account (Osherson, 1974-6) includes a fragment of modal logic, and Rips(1994, p. 336) has suggested that formal rules might be extended to deal with causalreasoning. Likewise, philosophers have proposed axiomatic systems for causal deductions(e.g., von Wright, 1973). Hence, causal deductions could depend on axioms (or “meaningpostulates”) of the following sort:If X causes Y, and Y prevents Z, then X prevents Z,whereX, Y, and Z, are variables that take states as their values.

The second answer is that you make causal inferences relying onpragmatic reasoningschemas(e.g., Cheng et al., 1986). For instance, the preceding axiom is framed instead as arule of inference:

X causes Y.

Y prevents Z.

[ X prevents Z.

This rule and others make up a pragmatic schema, and causal reasoning as a wholecould depend on several such schemas. The idea goes back to Kelley’s (1973) theory ofcausal attribution, which postulated such schemas for checking causal relations. Morris& Nisbett (1993), for example, formulated a schema that includes the following tworules:

If cause A is present then effect B occurs.

Cause A is present.

[ Effect B occurs.

and:

If cause A is present then effect B occurs.

Effect B does not occur.

[ Cause A is not present.

Inferences about causation tend to be easier than equivalent inferences based on conditionals,at least in Wason’s selection task (e.g., Markovits & Savary, 1992). Hence, Morris & Nisbett(1993) argue that schemas guide causal deduction, and that this claim is supported by the factthat graduate students in psychology improve in causal reasoning whereas those in philos-ophy do not. These phenomena, however, are open to alternative explanations–content andexperience may, for example, enable individuals to flesh out their models of possibilitiesmore explicitly (cf. Green & Over, 2000).

The third answer is that naive reasoners make causal deductions, not by using rules orschemas, but by constructing mental models. Given the appropriate temporal constraints and,say, the following mental model of possibilities:


a b c

¬a ¬b c

¬a b ¬c

they can validly infer:A causes C,because the model contains each of the possibilitiesrequired for this relation. In practice, naive individuals may not construct fully explicitmodels. The theory accordingly postulates:

The principle ofcausal deduction:Causal deductions are based on models of the premises, and with complex premises, these

models will tend to be mental models rather than fully explicit models. Granted theappropriate temporal constraints, a conclusion is valid if the set of premise possibilitiescorresponds to the set for the conclusion.

2.6. The predictions of the theory

The model theory makes three main empirical predictions. First, it predicts that themeanings of causal relations are modal, and so naı¨ve individuals should consider that eachsort of causal relation rules out certain states of affairs as impossible. In contrast, probabi-listic accounts of the meaning of, say,A will cause B,are compatible with any possibility,because only the relative frequencies of possibilities matter. Second, the model theorypredicts that causes and enabling conditions differ in meaning. Hence, naı¨ve individualsshould judge that different possibilities are compatible with assertions of the form,A willcause BandA will allow B (see Table 2). Likewise, they should draw different deductiveconclusions from the two sorts of assertion. In contrast, the theories summarized in Table 1draw no such distinction in the meaning and logic of causes and enabling conditions.Similarly, probabilistic theories have difficulty in distinguishing between causes and en-abling conditions, and predict that no necessary conclusions will be drawn from them. Third,the principle of causal deduction implies that some valid deductions should be easier thanothers: those based on mental models should be drawn more accurately than those that callfor fully explicit models. Theories based on schemas and rules might be framed to make thesame prediction. Only the model theory, however, predicts the occurrence of “illusory”inferences arising from the failure to represent what is false. In what follows, we describe aseries of experiments designed to test these predictions.

3. Studies of causal meanings

The aim of our initial experiment was to test the model theory’s prediction that naiveindividuals should treat some states as possible and some as impossible for each causalrelation, and the prediction thatcausediffers in meaning fromallows.In addition, however,according to the principle of truth, the first true possibility the participants should envisageshould correspond to the explicit mental model of the relation. Hence, forA will cause B,thefirst possibility that the participants envisage should be A and B; forA will prevent B,the firstpossibility should be A and not-B; forA will allow B, the first possibility should be A and


B; and forA will allow not B, the first possibility should be A and not-B. Because it shouldbe quite hard to flesh out the mental models to make them fully explicit, the status of theremaining true possibilities, which correspond to those only in fully explicit models, should bemore difficult for the participants to determine, and so they may fail to enumerate them correctly.

3.1. Experiment 1: modal meanings

To understand the meaning of an assertion is at least to grasp what it allows as possibleand what it rules out as impossible. Because no previous study had examined this aspect ofcausal relations, our first experiment was a study of possibilities. The participants’ task wasto list what was possible and what was impossible given each of the four weak causalassertions. We distinguish this task from one in which participants have to decide whetheran assertion is true or false in various situations. This second task calls for a meta-linguisticgrasp of the predicates “true” and “false,” whereas listing possibilities, according to themodel theory, taps into a more fundamental ability to grasp the meaning of assertions (seeJohnson-Laird & Barres, 1994).

The assertions in the experiment concerned singular causal relations with unknownoutcomes, and so they were of the form:

1. A will cause B.2. A will prevent B.3. A will allow B.4. A will allow not B.

We also included a control assertion, which was a tautology of the following form:

5. A or not A will cause B or not B.

which is compatible with all four possibilities. To ensure that there was no confoundingbetween contents and causal relations, we used five different contents rotated over the fiveassertions.

Method.The participants listed both possible cases and impossible cases for the 25 asser-tions, which were presented in a different random order to each participant. The five contents,which were rotated over the relations, concerned health and the performance of mechanicalsystems. We aimed to select materials that were meaningful to the participants but that madesense in all of the causal relations. The contents are illustrated here:

1. Generating a strong reactivity will cause damage to the reactor.2. Having a spinal implant will prevent Vivien from being in pain.3. Using the new fuel will allow the engine to survive the test.4. Eating protein will allow her not to gain weight.5. Running the new application will cause the computer to crash.

The participants were presented with an assertion, and their task was to write down whatwas possible and what was impossible given the assertion. They were free to write the itemsin any order. And they were told explicitly that there were four cases to consider for each


sentence, and they were urged to try to deal with all of them. We tested 20 Princetonundergraduates individually, and they were paid $4 for their participation.

Results and Discussion.Table 4 presents the most frequent interpretations for each of the fivesorts of assertion, and the numbers of participants who made each interpretation three ormore times out of the five trials. The results corroborated the predictions of the model theory.First, the participants generated both true and false possibilities for the causal relations (19participants did so more often than not, Binomial p, .0001). Second, the participants tendedto start their list with the possibility corresponding to the explicit mental model of the causalrelation (all 20 participants did so more often than not,p 5 .520). Third, the participantssometimes failed to list all four of the possibilities as either true or false. They listed a meannumber of 3.75 possibilities, and seven of the participants failed to list all four possibilitieson at least one occasion. As Table 4 shows, the participants tended to make “strong”interpretations, that is, to minimize the number of possibilities that are true. Overall, theirinterpretations coincided with the model theory’s predictions. There are 16 possible inter-pretations, and so the chance probability of making a predicted strong or weak interpretationis 1/8. There was a significant tendency to make the predicted interpretations forcause(Binomial, p , 1 in a billion) and forprevent(Binomial, p , 1 in a billion). The onlyunexpected result was the tendency ofallow andallow not to elicit strong interpretations.Nevertheless, there was a reliable tendency to treatallow as signifying either all possibilitiesor the three possibilities taking into account the implicature (Binomial,p , .0003), and totreatallow not as signifying the predicted interpretation (Binomial,p , .01).

If causal relations are probabilistic, then all four cases are possible and nothing isimpossible, because it is only the relative frequencies of the different cases that matter. But,contrary to probabilistic theories, the participants generated both true and false possibilities

Table 4The patterns of response to the five causal relations in Experiment 1, and the number of participants (n5 20)generating each of them on at least three trials out of five. The table shows only those interpretations madeby more than one participant.

The participants’ interpretations

Listed as possible a b a b a b a b a ba ¬b a ¬b a ¬b a ¬b a ¬b

¬a b ¬a b ¬a b ¬a b ¬a b¬a ¬b ¬a ¬b ¬a ¬b ¬a ¬b ¬a ¬b

Listed as impossible a b a b— a ¬b a ¬b

¬a b ¬a b¬a ¬b ¬a ¬b Totals

Tautology: 13 6 19A will cause B: 9 10 19A will allow B: 4 10 5 19A will prevent B: 3 14 17A will allow not B: 10 7 17


for each causal relation. Skeptics might suppose that this result reflects the demand charac-teristics of the experiment, and particularly the instruction to list what was possible andimpossible. However, more than half the participants were prepared to list all four possibil-ities as true in the case of the tautology. Likewise, they showed a reliable consensus aboutwhat possibilities were ruled out by each sort of assertion. Hence, the demand characteristicsof the experiment cannot explain the results. The results also showed that naı¨ve individualsdo distinguish between the meaning of causes and enabling conditions (contrary to the theoriesin Table 1). We carried out a similar experiment using general causal claims, and its resultsalso corroborated the model theory. In sum, both experiments supported the model theory.

3.2. Experiment 2: causes and enabling conditions

If individuals are given a set of possibilities, it is plausible to suppose that they should beable to produce an appropriate causal description of them. But, previous studies in whichparticipants have to describe sets of possibilities have merely resulted in descriptions of eachseparate possibility in a long disjunction (see e.g., Byrne & Johnson-Laird, 1992). Cheng &Novick (1991) used an alternative way to give individuals a set of possibilities. Theypresented descriptions of the circumstances without using any causal expressions. Theparticipants’ task was to identify the causes and the enabling conditions within thesedescriptions. The model theory predicts that they should be able to carry out this task.Moreover, if the theory is correct, then they ought to be able to discern the differencebetween the two in the same circumstances. Cheng and Novick reported such an effect, butthey relied on scenarios with constant enabling conditions and inconstant causes. Our nextexperiment accordingly examined circumstances in which neither causes nor enablingconditions were constant.

The aim of the experiment was to determine whether naı¨ve individuals could distinguishcauses and enabling conditions when neither was constant in the circumstances of the samescenario. Consider, for example, the following description:

1. Given that there is good sunlight, if a certain new fertilizer is used on poor flowers, thenthey grow remarkably well. However, if there is not good sunlight, poor flowers do notgrow well even if the fertilizer is used on them.

Logically speaking, we can paraphrase and abbreviate this description as follows:If sunlight then if fertilizer then growth; and if not sunlight then not growth.

The corresponding circumstances are the following fully explicit models of the possibilities,as constructed by the computer program:

Sunlight Fertilizer Growth

Sunlight ¬Fertilizer Growth

Sunlight ¬Fertilizer ¬Growth

¬Sunlight Fertilizer ¬Growth

¬Sunlight ¬Fertilizer ¬Growth


In these circumstances, sunlight is an enabling condition for the flowers to grow well:

Sunlight Growth

Sunlight ¬Growth

¬Sunlight ¬Growth

But, the presence of sunlight also makes the fertilizer act as a cause of the flowers growingwell.

In contrast, consider the following description:

2. Given the use of a certain new fertilizer on poor flowers, if there is good sunlight thenthe flowers grow remarkably well. However, if the new fertilizer is not used on poorflowers, they do not grow well even if there is good sunlight.

This yields the following fully explicit models of the possibilities:

Sunlight Fertilizer Growth

¬Sunlight Fertilizer Growth

¬Sunlight Fertilizer ¬Growth

Sunlight ¬Fertilizer ¬Growth

¬Sunlight ¬Fertilizer ¬Growth

The causal roles have been swapped around: the fertilizer is the enabling condition and itspresence makes the sunlight act as the cause of the flowers’ growth. In these scenarios, causeand enabling condition differ in their meaning and logic. The experiment accordinglyreplicated Cheng & Novick’s (1991) study but used scenarios in which neither causes norenabling conditions were constant.

Method. We prepared eight pairs of descriptions, such as the fertilizer examples above, inwhich there were two precursors to the effect and their respective roles as enabling conditionand cause were counterbalanced in the two descriptions. We also prepared versions of thepairs of descriptions in which we reversed the order of mention of cause and enablingcondition. Thus, corresponding to the preceding pair of examples, there were descriptions asfollows:

19. If a certain new fertilizer is used on poor flowers, then given that there is goodsunlight, they grow remarkably well. However, if there is not good sunlight, poorflowers do not grow well even if the fertilizer is used on them.

29. If there is good sunlight, then given the use of a certain new fertilizer, poor flowersgrow remarkably well. However, if the new fertilizer is not used on poor flowers, theydo not grow well even if there is good sunlight.

The participants acted as their own controls and read eight descriptions that each con-cerned a cause, an enabling condition, and an effect. They also read two filler items–one inwhich there were two joint causes and one in which there were no causes. Each participantencountered just one version of a particular description, but two instances of the four sorts


of description in the experiment as a whole. The order of presentation was randomized foreach participant.

We tested 20 Princeton Undergraduates, who were fulfilling a course requirement. Theirtask was to identify the enabling condition and the cause in each scenario. As in Cheng andNovick’s study, the participants were given a minimal instruction about the differencebetween causes and enabling conditions. They were told that the cause of an eventbringsabout the event,and the enabling conditionmakes the event possible,but these terms did notoccur in the scenarios themselves. The participants were told that some passages did notcontain an enabling condition.

Results and discussion.The participants correctly identified the enabling conditions andcauses on 85% of trials, and every participant was correct more often than not (p 5 .520).Likewise, all the eight scenarios conformed to this trend (p 5 .58). Hence, individuals givendescriptions of scenarios that make no reference to causation can distinguish enablingconditions from causes. Contrary to a long-established tradition from Mill (1874) onwards,we conclude that causes and enabling conditionsdo differ in meaning, that naive individualscan distinguish between them, and that they can base their distinction on independentdescriptions of the relevant sets of possibilities. These descriptions rely essentially onconditionals, and, unlike those of Cheng and Novick, the contrast is not based on makingenabling conditions constant in the scenario and causes inconstant. It follows that none of thecontrasts in Table 1 is essential to the distinction between causes and enabling conditions.They can at best make predictions about only one of our matched pairs of scenarios in whichthe causal roles are swapped around. Likewise, as we will show in the General Discussion,the results count against probabilistic theories of causation. Are there cases where priorknowledge blocks the swapping around of cause and effect (Daniel Schwartz, personalcommunication)? Indeed, there are likely to be such cases. Knowledge modulates theinterpretation of assertions and can rule out possibilities compatible with them (see Johnson-Laird & Byrne, 2001, for an account of this process). Thus, consider the following descrip-tion:

Given that there is sunlight, if there is water, then the plants grow. However, if there is nosunlight, the plants do not grow even if there is water.

It ought to yield possibilities corresponding to those for description 1 above. However, yourknowledge of the need for water is likely to eliminate the possibility:

Sunlight ¬Water Growth

and so you will treat sunlight and water as joint causes of growth.

4. Studies of causal reasoning

Reasoning is based on the representation of assertions. In this section, we report threestudies that tested the predictions of the model theory about reasoning from causal assertions.The results of the preceding studies showed that naı¨ve individuals distinguish the differencein meaning betweenA will cause BandA will allow B. This difference in meaning, which


is predicted by the model theory, should also be borne out in logical reasoning. If naı¨veindividuals are given the following premises:

Eating protein will cause her to gain weight.She will eat protein.

the model theory predicts that they should tend to draw the conclusion: She will gain weight.But, if they are given analogous premises based onallow:

Eating protein will allow her to gain weight.She will eat protein.

the theory predicts that they should be less likely to draw the conclusion: She will gainweight. Likewise, the following premises based onprevent:

Eating protein will prevent her from gaining weight.She will eat protein.

should tend to elicit the conclusion: She will not gain weight. But, the analogous premisesbased onallow-not should be less likely to elicit this conclusion. The model theory makesanalogous predictions about inferences based on the categorical denial of the proposition thatoccurs in the consequent of the causal claim. Thus, premises of the form:

A will cause B.

Not-B.

should be more likely to elicit the conclusion: Not-A, than analogous premises based onallow. Likewise, premises of the form:

A will prevent B.

B.

should be more likely to elicit the conclusion: Not-A, than analogous premises based onallow-not.

The principle of causal deduction (see Section 2) implies that some causal deductionsshould be easier than others. In particular, those for which mental models suffice should yield ahigh percentage of correct conclusions. For example, consider a problem of the following form:

A causes B.

B prevents C.

What, if anything, follows?

It should be easy to draw a conclusion of the form: A prevents C, because the conclusionholds in the mental model of the premises. As the computer program shows, the premises:

A causes B: a b

. . .

B prevents C: b ¬c

. . .

yield a single integrated mental model:


a b ¬c

. . .

where each row represents a possibility in the model. This model contains the possibilitiescorresponding toA prevents C.This conclusion is valid, because it holds in the fully explicitmodel of the premises:

a b ¬c

¬a b ¬c

¬a ¬b c

¬a ¬b ¬c

In contrast, consider the following problem:

A prevents B.

B causes C.


The mental model of the premises is as follows:

a ¬b

b c

. . .

The possibility containing A does not contain C, and so reasoners should draw the conclu-sion: A prevents C. The conclusion is wrong, however. The fully explicit model of the twopremises is:

a ¬b c

a ¬b ¬c

¬a b c

¬a ¬b c

¬a ¬b ¬c

As this model shows, A doesnotprevent C. In fact, there is no causal relation between them.

4.1. Experiment 3: the logical properties of causes and enabling conditions

Experiment 3 was designed to test the predictions about the difference between inferencesbased oncauseandallow, andpreventandallow not.The participants were given pairs ofpremises using these four causal relations coupled with categorical assertions of all four sorts(the antecedent state, the consequent state, and their respective negations). The four keycomparisons for the model theory are shown in Table 5 below. The other eight inferences in


the set of 16 are, in effect, “filler” items, because their validity depends on whether reasonersmake strong interpretations of the causal relations.

Method. The participants acted as their own controls and carried out sixteen problems. Eachproblem consisted of two premises followed by a question, for example:

Eating protein will cause her to gain weight.

She will eat protein.

Will she gain weight?

Yes. No. Perhaps yes, perhaps no.

The participants were told to circle “yes” if the proposition in the question followed logicallyfrom the premises, that is, the proposition must be true given that the premises are true, tocircle “no” if the negationof the proposition in the question followed logically from thepremises, that is, the proposition must be false given that the premises are true, and to circle“Perhaps yes, perhaps no” if neither the proposition in the question nor its negation followedlogically from the premises. The problems were composed from the four causal relationspaired with the affirmation or denial of the antecedent or consequent proposition. We devised16 sets of contents, half of which concerned singular events about persons and half of whichconcerned singular events about mechanical systems. We assigned them twice at random tothe 16 forms of inference in order to produce two versions of the materials.

The participants were 129 of the best high school graduates in Italy, with a mean age ofapproximately 19 years, who were applicants to the Scuola Superiore Sant’Anna of Pisa, ahighly selective Italian university.

Results and discussion. Table 5 presents the percentages of predicted results for the crucialproblems. In each case, the comparisons were in the direction that the model theorypredicted, and each of them was highly significant on a Sign test, that is, considerably lessimprobable than one in a billion. In particular, given premises of the form: A will cause B,

Table 5The 8 crucial forms of inferential problems in Experiment 3. The table presents the percentages of theparticipants who drew the responses shown in the table.

The second premise

A Not-B

The first premise:A will cause B [ B: 93 [ Not-A: 93A will allow B [ B: 30 [ Not-A: 47

The second premise

A BThe first premise:A will prevent B [ Not-B: 85 [ Not-A: 82A will allow not B [ Not-B: 36 [ Not-A: 36


A, reasoners drew the conclusion,B, reliably more often than from premises of the form:Awill allow B, A (85 participants fit the prediction, 2 went against it, and the rest were ties).Given premises of the form:A will cause B, not-B,reasoners drew the conclusion,not-A,reliably more often than from premises of the form:A will allow B, not-B(64 participants fitthe prediction, 5 went against it, and the rest were ties). Similarly, given premises of theform: A will prevent B, A,reasoners drew the conclusion,not-B, reliably more often thanfrom premises of the form:A will allow not B, A(70 participants fit the prediction, 6 wentagainst it, and the rest were ties). Given premises of the form:A will prevent B, B,reasonersdrew the conclusion,not-A,reliably more often than from premises of the form:A will allownot B, B(64 participants fit the prediction, 6 went against it, and the rest were ties). Theseresults show that the pattern of inferences fromcauseandallow are quite distinct, and thatthe pattern of inferences frompreventandallow-notare also quite distinct. We conclude thatthe model theory’s account of the difference in meaning between the causal relations isupheld. Causes and enabling conditions differ in meaning and hence in the inferences thatthey support. The result is incompatible with probabilistic theories – a point to which wereturn in the General Discussion, and it is also incompatible with the many theories thatpresuppose that causes and enabling conditions do not differ in meaning (see Table 1).

4.2. Experiment 4: deductions from two causal premises

The goal of Experiment 4 was to test the principle of causal deduction. The participants’task was to draw conclusions in their own words from pairs of premises. The first premise

Table 6The inferences in Experiment 4, their mental models, the conclusions they predict, and the frequencies withwhich the participants (N5 20) drew them. Valid conclusions are in capital letters.

Second premise First premise

A causes B A allows B A prevents B Not-A causes B

B causes C a b c a b c a¬b ¬a b c. . . a b c . . .

A CAUSES C: 20 A allows . . . C: 18 A . . .prevents CL 19 Not-A CAUSES C: 20

B allows C a b c a b c a ¬b ¬a b ca b a b b c ¬a b

. . . a b . . .. . . . . .

A allows C: 19 A ALLOWS C: 19 APREVENTS C: 20Not-A allows C: 20

B prevents C a b ¬c a b ¬c a ¬b ¬a b ¬c. . . a b ¬c . . .

. . . . . .A PREVENTS C: 20 A allows not-C: 14 A prevents C: 15 Not-A PREVENTS C: 20

Not-B causes C a b a b a¬b c ¬a b¬b c a ¬b c . . . ¬b c

. . . a . . .¬b c. . .

A prevents C: 9 AALLOWS Not-C: 12 A CAUSES C: 17 Not-A prevents C: 15


interrelated two states of affairs using one of the four distinct causal relations (A causes B,A allows B, A prevents B,andNot-A causes B), and the second premise interrelated two statesof affairs, B and C, using one of the same set of causal relations. Table 6 presents the16 pairs of premises and the predictions of the computer program based on mentalmodels. It predicts that reasoners should draw a conclusion in all 16 cases. Half of theseconclusions are valid, but half of them are invalid. Those inferences should be difficultfor which a discrepancy occurs between the conclusion based on the mental model of thepremises and the conclusion based on the fully explicit model of the premises. Naiveindividuals should tend to draw the conclusion predicted by the mental model. Neitherformal rules nor pragmatic schemas, as they are currently formulated, make any pre-dictions about these deductions.

Method. Each participant carried out in a random order all 16 possible inferences based onthe four sorts of premise in the following figure:

A - B.

B - C.

The content of the premises consisted of psychological terms that were familiar to theparticipants, but not so familiar that they would elicit strong beliefs about the truth or falsityof the premises. We used two random allocations of the contents to the set of 16 problems.A typical problem was as follows:

Obedience allows motivation to increase.

Increased motivation causes eccentricity.


The instructions made clear that although the contents were sensible, it was not crucial forthe participants to know precisely what each term meant. Their task was to state in their ownwords whatever conclusion, if any, followed from the premises, that is, a conclusion must betrue given that the premises were true. We tested individually 20 Princeton undergraduates,who received $4 for participating in the experiment.

Results and discussion.Table 6 presents the numbers of participants drawing the mainconclusions to each of the sixteen inferences. The participants tended to draw the predictedconclusions whether they were valid (93% of conclusions) or invalid (80% of conclusions).Each participant drew more predicted than unpredicted conclusions (p 5 0.520) and 15 outof the 16 inferences yielded more predicted than unpredicted conclusions (Sign test,p , .0005). In sum, the results supported the principle of causal deduction. The one inferencefor which the model theory’s prediction failed was of the form:

A causes B.

Not-B causes C.

The model theory predicts the invalid conclusion: A prevents C, which was drawn by nineof the participants. Eight other participants drew the weaker conclusion: A allows not-C. Thisconclusion is valid, ignoring the implicature that not-A does not allow not-C.


Could the participants have made their responses under the influence of the particularverbs that occurred in the premises? For example, given premises of the form:

A causes B.

B causes C.

they might have been biased to draw a conclusion with the same verb:A causes C.Althoughwe cannot rule out the possibility that such “atmosphere” effects sometimes occur, theycannot explain the results as a whole. For example, given premises of the form:

Not-A causes B.

Not-B causes C.

atmosphere predicts the invalid conclusion: Not-A causes C. The model theory, however,predicts a different invalid conclusion: Not-A prevents C, which the majority of participants(75%) drew. Alleged atmosphere effects in other domains of reasoning are likewise open toalternative explanations based on the use of models in reasoning (Bucciarelli & Johnson-Laird, 1999).

4.3. Experiment 5: illusory inferences about causal relations

The previous experimental results could conceivably be explained by a theory based onformal rules or pragmatic schemas. So, is there any way to strengthen our claim thatreasoners rely on mental models? The answer depends on an unexpected prediction. Ac-cording to the principle of truth, mental models fail to represent what is false, and so certainpremises give rise toillusory inferences: most people draw one and the same conclusion,which seems obvious, and yet which is wrong. Such illusory inferences occur in deductivereasoning based on sentential connectives (Johnson-Laird & Savary, 1999) and quantifiers(Yang & Johnson-Laird, 2000). They occur in modal reasoning about possibilities (Goldvarg& Johnson-Laird, 2000), in probabilistic reasoning (Johnson-Laird et al., 1999), and inreasoning about consistency (Johnson-Laird et al., 2000). The illusions provide a strongsupport for the model theory, and they are contrary to current rule theories. These theoriesuse only valid rules of inference (see e.g., Rips, 1994; Braine & O’Brien, 1998), and so theycannot account for a phenomenon in which most people draw one and the sameinvalidconclusion.

Because illusory inferences occur in reasoning about possibilities, they should also occurin causal reasoning. As an example of a potential illusion, consider the following problembased on singular causal assertions:

One of these assertions is true and one of them is false:

Marrying Evelyn will cause Vivien to relax.

Not marrying Evelyn will cause Vivien to relax.

The following assertion is definitely true:

Vivien will marry Evelyn.


Will Vivien relax? Yes/No/It’s impossible to know.

The mental models of the initial disjunction of premises are as follows:

Marry Relax

¬Marry Relax

The premise that is definitely true eliminates the second of these models, and so it seems tofollow that Vivien will relax. But, the models of the initial disjunction fail to represent whatis false, that is, when the first premise is true, the second premise is false, and vice versa. Ifit is false that marrying Evelyn will cause Vivien to relax, but true that Vivien will marryEvelyn, then Vivien maynot relax. Hence, the premises do not imply that Vivien will relax.The conclusion is an illusion. The correct response is that it is impossible to know what willhappen. The aim of the experiment was to test whether naı¨ve individual succumbed to theillusory inferences.

Method. Each participant carried out four inferences in a random order: the illusory inferenceabove, an analogous illusion based onprevent,and two control problems for which thefailure to represent falsity should not yield errors (see Table 8). The problems concernedeveryday matters, as in the example above, and the contents were allocated twice to the fourforms of inferences. We tested 20 Princeton Undergraduates individually, who were fulfillinga course requirement. Their task was to state what conclusion, if any, followed from thepremises. The instructions emphasized that in each initial pair of premises one assertion wastrue and one was false.

Results and discussion.Table 7 presents the percentages of participants making each re-sponse. One participant responded “impossible to know” to all the problems, including thecontrols, and so werejected his data. The remaining participants tended to succumb to theillusions, making them more often than one would expect by chance (Binomial test,p ,.02). Likewise, they were correct more often on the control problems than on the illusoryinferences (p 5 .519). Readers may worry that the participants merely overlooked thatone of the initial assertions was true and one was false. The instructions made this pointas clear as possible, and other studies have deliberately varied the rubrics and yet stillthe participants erred. Their think-aloud protocols showed that they had not overlookedthe nature of the rubrics (Johnson-Laird & Savary, 1999). The results accordinglysupport the model theory, but they are contrary to theories based on formal rules orschemas. These theories contain only logically impeccable rules, and the only way inwhich they could yield invalid conclusions is by a mistake in their application. Suchmistakes, as Rips (1994, p. 385) has rightly pointed out, should have “diverse sources,”and so “a unified account of errors seems extremely unlikely.” It strains credulity toimagine that errors of this sort could lead most reasoners to one and the same invalidconclusion. In contrast, the model theory predicts the illusions on the grounds thatmental models fail to represent what is false.


5. General discussion

We have advanced a new theory of causality as conceived in everyday life by people withno training in philosophy or logic. The theory gives an account of the meaning of causalrelations, their mental representation, and their deductive consequences. It depends on fiveprinciples:

1. Truth: People represent propositions by constructing mental models in which eachmodel represents what is true in each possibility compatible with the premises.

2. Temporal constraint: If A has a causal influence on B, then B does not precede A intime.

3. Causal modalities: The meaning of a causal relation between two states of affairs, Aand B, concerns what is possible and what is impossible in their co-occurrences. Theprinciple applies to general causal claims (represented in a single model of possiblestates) and to singular causal claims (represented in a set of models of possibilities).

4. Circumstantial interpretation: Causal interpretation depends on how people conceivethe circumstances of states, that is, on the particular states that they consider to bepossible, whether real, hypothetical, or counterfactual.

5. Causal deduction: Individuals base their causal deductions on mental models of thepremises, inferring whatever conclusion, if any, has the possibilities corresponding tothose of the premises.

Does the mere existence of the relevant set of possibilities satisfying the temporalconstraint suffice for a causal relation? Or, could there be cases that satisfy our analysis butthat are not causal? “Many things,” Cheng (1997, p. 367) writes, “follow one anotherregularly, yet one does not infer a causal relation between them.” She cites the case of arooster that crows every day just before sunrise. On our analysis, however, the claim that therooster’s crowing causes the sun to rise means that the rooster cannot crow at any time of

Table 7The two illusions and the two control problems of Experiment 5 (stated in abbreviated form). The tableshows the percentages of participants (N5 19) making each response.

Illusions Control problems

1. One is true and one is false: 19. One is true and one is false:A will cause B. A will cause B.Not-A will cause B. Not-A.

Definitely true: Definitely true:A A

[ B: 68 [ B: 100Impossible to know: 32

2. One is true and one is false: 29. One is true and one is false:A will prevent B A will prevent B.Not-A will prevent B Not-A.

Definitely true: Definitely true:A A

[ Not-B 53 [ Not-B 89Impossible to know: 47 Impossible to know: 11


day, including midnight, without the sun rising shortly thereafter. In a fairy tale, such a magicrooster would indeed be said to cause the sunrise (without presupposing any causal mech-anism). Some alternative views about causation are that causes and enabling conditions donot differ in meaning, that causation is a probabilistic notion, that its meaning refers to amechanism, that deductions about causal relations depend on schemas or rules of inference,and that causal meanings and principles of reasoning differ from one domain to another. Ifour theory is right, then each of these views, which we discuss in turn, is wrong.

5.1. Causes differ in meaning from enabling conditions

The model theory implies that there are four weak causal relations (A will cause B, A willprevent B, A will allow B,andA will allow not-B). Experiment 1 showed that individualsdistinguish between these relations. They tended to generate the predicted sets of possibilities(and impossibilities) for each relation. From Mill (1874) onwards, however, the consensushas been that causes and enabling conditions do not differ in meaning or logic. This view hasin turn led psychologists to search for some other difference between them. They haveproposed many putative distinctions–enabling conditions are normal and causes abnormal,enabling conditions are common and causes rare, enabling conditions are constant and causesinconstant, and so on (see Table 1). But, as the model theory predicted, naı¨ve individuals inExperiment 1 distinguished between their meanings. Given an assertion, such as: Using thenew fuel will cause the engine to survive the test, all but one of the participants listed asimpossible the following situation: Use of the new fuel and the engine does not survive thetest. But, given the assertion: Using the new fuel will allow the engine to survive the test,most participants listed as impossible the following situation: Not using the new fuel and theengine survives the test.

The model theory postulates that causal status in complex cases is determined by the setof possibilities as a whole, that is, the circumstances. In one set of circumstances, forexample, if there is sunlight, then fertilizer causes flowers to grow. In a contrasting set, thecausal roles can be swapped round: if there is fertilizer, sunlight causes the flowers to grow.An ideal way to test the difference would be to ask people to put into their own words therelevant sets of possibilities, but there is no magical way to inject a set of possibilities intosomeone’s head. In Experiment 2, we therefore described them in other terms, that is,without using any causal expressions. The participants’ task was to identify which was thecause and which was the enabling condition. They were able to do so in a highly reliableway. The experiment thus replicated Cheng & Novick (1991) but with an importantdifference. It showed that individuals can distinguish between causes and enabling condi-tions when neither is constant in the circumstances. Likewise, as the experiment showed,they may judge that a passive agent, for example, sunlight or the presence of oxygen, is thecause, and that an active agent, for example, fertilizer or a spark, is the enabling condition.If there is tendency to judge active agents as causes in everyday life, then it may reflect apragmatic shortcut rather than a full understanding of the circumstances.

The distinction in meaning between causes and enabling conditions yields different logicalconsequences. Causal premises such as:


Eating protein will cause her to gain weight.


imply the consequent: Therefore, she will gain weight. But, enabling premises such as:

Eating protein will allow her to gain weight.


do not imply the consequent. She may, or may not, gain weight. Experiment 3 corroboratedthese predictions: the two sorts of claim are logically distinct. The factors invoked bypsychologists to distinguish between causes and enabling conditions (see Table 1) are neithernecessary nor sufficient to explain the difference between their logical properties. Thedifference in their meanings suffices.

5.2. The meanings of causal relations are not probabilistic

Just as a philosophical view about causation led psychologists to discount a semanticdistinction between causes and enabling conditions, so too another philosophical view hasled them to hold that the meaning of causal relations in everyday life is probabilistic.Probabilistic theories may be viable in metaphysics and in scientific conceptions of causa-tion, especially since the development of quantum mechanics (see e.g., von Mises, 1957,Sixth lecture). Probabilities may enter into the induction of causal relations from observa-tions (Pearl, 1988; Shafer, 1996; Cheng, 1997; Lober & Shanks, 1999). Likewise, a causalassertion may differ in its probability, that is, some causal assertions are highly probablewhereas others are highly improbable. But, are we to suppose that causal relations them-selves havemeaningsthat are probabilistic?

This view would have astonished Hume (1748/1988), who took a causal claim to applyuniversally with a constant conjunction of cause and effect. It would have astonished Kant,who argued that causation was an a priori notion which demands “that something, A, shouldbe of such a nature, that something else, B, should follow from it necessarily” (Kant,1781/1934, p. 90). It would have astonished Mill, who wrote: “The invariable antecedent istermed the cause; the invariable consequent, the effect” (Mill, 1874, p. 237). Indeed, Russell(1912–13) took the view that the concept of causation should be expurgated from philoso-phy, because it had been replaced by probabilistic correlations in science. That the conceptof cause itself might be probabilistic appears to be a doctrine unique to the world postquantum mechanics.

The principal evidence lending support to the probabilistic doctrine is that people assentto causal claims even when they know there are exceptions to them. Loose generalizationsare endemic in daily life. Hence, most people assent to the proposition:

Smoking causes lung cancer

even though they know that not everyone who smokes gets the disease. But, most people arealso likely to assent to the more accurate proposition:

Smoking often causes lung cancer.


Readers who agree that this assertion is more accurate have conceded the main point: ifcauses were intrinsically probabilistic, then the two assertions would not differ in meaning.Another factor in the use of loose causal generalizations may be that people are well awarethat many causes in everyday life yield their effects only if the required enabling conditionsare present and the potentially disabling conditions are absent. Naive individuals, as Cum-mins (1995, 1998) has shown, are sensitive to these factors. Hence, when people assent tothe loose generalization about smoking, they are granting the effect other things being equal.As Cummins remarks, they mean that the causal relation holds unless some disablingcondition is present.

In our view, a probabilisticmeaningof causality does not accord with everyday usage, asseveral strands of evidence show. The first strand of evidence is that naı¨ve individuals inExperiment 1 judged that certain possibilities are ruled out by causal assertions. Given, forexample, the assertion: Running the new application will cause the computer to crash, theylisted as impossible the following situation: Running the new application and the computerdoes not crash. Suppose on the contrary that the probabilistic theory were correct. It wouldfollow that the causal assertion means merely that the probability of the computer crashinggiven that one runs the new application is higher than the probability of it crashing given thatone does not run the new application. In this case, it is possible that one runs the newapplication and the computer does not crash. The only way to refute the causal claim wouldbe to make a set of observations to show that the relative frequencies of crashes supportedthe difference between the two conditional probabilities. Defenders of the probabilisticapproach might counter that the “demand characteristics” of Experiment 1 forced theparticipants to list both what is possible and what is impossible. But, this claim is refuted bythe fact that the majority of the participants treated the tautology as consistent with allpossibilities, that is, they did not list any situation as impossible in this case. Jonathan Evans(personal communication) has suggested that the use of singular events rather than generalcausal claims might have discouraged probabilistic interpretations in Experiment 1. In fact,we have run a study with general claims that yielded very similar results. Moreover, ifcausation is a probabilistic notion, then it should be probabilistic for both singular andgeneral claims. Consider the following problem:

Smoking causes lung cancer.

Pat smoked but did not get lung cancer.

Why was that?

As we observed anecdotally, people tend to make the following sorts of response: PerhapsPat had a strong resistance to cancer, he might not have smoked much, or he may have givenup smoking. They do not respond: Because that is the nature of causation. Yet, this answeris correct according to the probabilistic theory. In short, Hume (1739/1978) may have beenright when he argued that people treat chance as a case of a hidden cause.

The second strand of evidence derives from the distinction between causes and enablingconditions. Consider a set of possibilities stated with their frequencies of occurrence (out of100), as in the following partition:


Sunlight Fertilizer Growth 20

Sunlight ¬Fertilizer Growth 20

Sunlight ¬Fertilizer ¬Growth 20

¬Sunlight Fertilizer ¬Growth 20

¬Sunlight ¬Fertilizer ¬Growth 20

It follows that:

p(Growth ? Sunlight). p(Growth ? ¬Sunlight), i.e., .66. 0

p(Growth ? Fertilizer) . p(Growth ? ¬Fertilizer), i.e., .5. .33

Hence, both sunlight and fertilizer are causes according to the probabilistic theory, thoughsunlight has the greater probabilistic contrast. Yet, as the model theory predicts, individualsin Experiment 2 judged sunlight to be the enabling condition and fertilizer to be the cause.The distinction between causes and enabling conditions might be reconstructed within aprobabilistic theory in the following way:A causes Bmeans that B is very probable givenA, and A allows B means that B is quite probable given A (Jonathan Evans, personalcommunication). This idea seems plausible, but it makes exactly the wrong predictions aboutthe example above. In fact, the probabilistic theory obliterates the distinction between causesand enabling conditions. Yet people are sensitive to this distinction, and so the probabilistictheory fails to account for the everyday meaning of causal relations.

A third strand of evidence demonstrates another difficulty for the probabilistic theory.When probabilities are held constant, a manipulation of content can yield different attribu-tions of causality (Legrenzi & Sonino, 1994; White, 1995; Koslowski, 1996). Such resultsare clearly inexplicable if causation is equivalent to an assertion about conditional proba-bilities.

A fourth stand of evidence comes from Experiment 3. It showed that naı¨ve individualstend to draw definite conclusions from causal assertions. Given a causal premise, such as:Eating protein will cause her to gain weight, and the assertion that she eats protein, themajority of participants concluded that shewill gain weight. But, if a causal assertion ismerely a statement of a high conditional probability, then the participants should haverefused to draw any deductive conclusion. At the very least, they should have qualified theiranswers in terms of probabilities.

A fifth strand of evidence is that the probabilistic theory cannot explain cases in which acause decreases the probability of an effect (see e.g., Salmon, 1980). Here is an example fromTooley (1987, p. 234–5). Disease A causes death with a probability of 0.1, and disease Bcauses death with a probability of 0.8. Each disease, however, confers complete immunity tothe other disease. Given that an individual is in a certain condition, he is bound to contracteither disease A or disease B. In fact, a particular individual in this condition contracteddisease A, and as a result died. If he hadn’t contracted disease A, then he would havecontracted disease B, and so his probability of dying would have been 0.8. Hence, the causeof his death (disease A), in fact, did not increase the probability of his death, but lowered it.

A final strand of evidence comes from a paraphrase. A claim such as: If there were no


gravity then planets would not orbit stars, is unequivocal. Yet, it can be paraphrased as:Gravity causes planets to orbit stars. Nothing is uncertain in the meaning of such causal claims.Indeed, to allow some uncertainty, one asserts: Gravity probably causes planets to orbit stars.

5.3. Do causal meanings refer to mechanisms?

At the core of the model theory is the modal principle that causes concern sets ofpossibilities governed by a temporal constraint. But what of the other metaphysical principleof causal powers or mechanisms? As we mentioned in Section 2, everyday causal assertionsoften concern “action at a distance,” and they sometimes deliberately deny the existence ofan underlying causal mechanism. We therefore argued that it may be mistaken to build thesemetaphysical principles into the everyday meaning of causality. Such a claim, however, doesnot deny the existence of causal mechanisms.

You understand causal relations better when you have access to a mechanism, that is, youhave a dynamic mental model that can unfold over time (Johnson-Laird, 1983, Ch. 15). Itallows you to simulate the sequence of events and to infer causal consequences: A will causeB, but B in turn may feed back and have a causal influence on A (Green, 2001). A mechanismalso provides a lower level of explanation. At one level, you know what the system does, andat one level down you know how it does it (see Miyake, 1986). Suppose, for example, thatyou can put your computer into sleep mode in different ways, such as pressing control1Aor control1B, or control1A1B. It seems that the two keys A and B have equivalent rolesgiven that you press control: Pressing key A or key B, or both, causes the computer to go tosleep. But, consider the mechanism at one level down, namely, the circuit. If all you canobserve are the positions of the keys and their effect on the computer, it is impossible toidentify the circuit. In principle, there are infinitely many distinct circuits in which the keysmight have their effects, just as there are infinitely many distinct ways in which to computeany computable function. If you can at least measure whether or not current flows througha key, you may be able formulate a description of the mechanism. You might discover, forinstance, that when key B is pressed, current flows through it and puts the computer to sleepindependently from the position of key A. But, when key B isnot pressed it completes aseries with key A, and so the computer goes to sleep only when A is pressed too. Hence, theonly effect of switch A is to close or to break this second circuit. This mechanism at a lowerlevel justifies the description: Pressing key B, or pressing key A when key B is not pressed,puts the computer to sleep.

What causes the current to flow in these various circuits? A causal mechanism itself maybe further decomposed into a lower level mechanism, and at each level reference is made tofurther causes. Hence, we can talk of a difference in potential that causes a flow of electronsin each of the circuits. But, this mechanism itself contains a causal claim: the potentialdifference causes the flow. Once again, we can ask in turn for its causal mechanism. And soon ad infinitum. Each mechanism at a lower level embodies a causal claim, and, like a child’sseries of “why” questions, we can go on asking for the mechanism underlying each answeruntil we run out of knowledge.

The morals are threefold. First, mechanisms are not part of themeaningof causalassertions, because causal assertions can deny their existence without contradiction. Second,


a causal mechanism itself embodies causal relations at a lower level than those of thephenomena for which it provides an account. To stipulate that a causal claim is an assertionthat a mechanism exists runs the risk of a vicious circle: you appeal to a set of causal relationsin order to give an account of the meaning of causation. Third, mechanisms and simulationsbased on their mental models provide a powerful way of inferring causal consequences. Theycan be crucial in inferring causation from correlations or other inductive observations (seee.g., White, 1995).

5.4. Causal deduction depends on models, not rules or schemas

Although some theorists argue that causal relations cannot be deduced, but only induced,we have shown that naı¨ve individuals do make causal deductions. A common sort of causaldeduction occurs when you use your background knowledge to infer a causal interpretationof a state. You know that an insulin injection prevents a coma in diabetes; your diabeticfriend gives herself such an injection; and you infer that she will not go into a coma. Ofcourse, your conclusion may be mistaken: all deductions based on empirical premises,whether causal or not, are defeasible. That is, they may have conclusions that turn out to befalse because a premise is false. Likewise, the deductive process is not always straightfor-ward. Santamaria, Garcia-Madruga, and Johnson-Laird (1998) gave participants a pair ofbelievable conditional premises, which each expressed a causal relation, such as:

If Marta is hungry, then she takes an afternoon snack.If Marta takes an afternoon snack, then she has a light dinner.

Both premises are believable, and they yield the following valid conclusion: If Marta ishungry, then she has a light dinner. Yet, the participants were reluctant to draw thisconclusion, presumably because it is unbelievable. It lacks the causal link (eating the snack)between its antecedent and consequent, and so it violates the normal relation between hungerand dinner.

Causal deductions could depend on formal rules of inference or on pragmatic reasoningschemas. Experiment 4, however, corroborated the principle of causal deduction–that naiveindividuals deduce causal relations from mental models of the premises. The experimentshowed that they tended to draw those conclusions supported by mental models of thepremises, whether or not the conclusions were valid. Experiment 5 established the occur-rence of illusory inferences based on causal premises. Given premises of the form:

One of the following assertions is true and one of them is false:A will cause B.Not-A will cause B.

This assertion is definitely true: A

most participants inferred invalidly: B will occur. These illusions are a crucial test of themodel theory. It predicts their occurrence because mental models represent only what is true(the principle of truth). Theories based on formal rules or pragmatic schemas, however,cannot account for the illusions. These theories postulate only valid rules of inference, andso they have no way to explain the systematic occurrence of invalid inferences.


5.5. Causal meanings and principles of reasoning do not differ from one domain toanother.

Throughout this article, we have presupposed a uniform account of causation and causalreasoning. A contrasting view is that causal reasoning differs from one domain to another.Similarly, individuals may rely on, say, pragmatic reasoning schemas when they haveknowledge of a domain, but on mental models or some other “weak” method when they haveno relevant knowledge. In fact, a study of how people explain inconsistencies suggests thatthere are strong uniformities across domains (see Legrenzi et al., 2001). In two experiments,the participants were presented with sets of inconsistent assertions, and their task was to rankorder the probability of seven different putative explanations of each inconsistency. Theparticipants tackled four scenarios from five different domains: physics, mechanics, biology,psychology, and socio-economics. They all rated an explanation consisting of a cause and aneffect as more probable than either the cause alone or the effect alone. This bias was uniformover all five domains. Likewise, in the present studies, no striking effects occurred as a resultof the content of the problems, for example, health problems versus mechanical problems inExperiment 1. There may be differences yet to be detected in causal reasoning depending ondomain or knowledge. So far, however, the hypothesis of uniform principles has survivedtesting.

5.6. Induction and the model theory

The model theory has implications for the process of inducing causal relations fromobservations. Knowledge of explicit possibilities, as we have seen, allows individuals todeduce an appropriate causal relation from observations. It can also override data about therelative frequencies of different sorts of event (see Section 2). But the theory of meaning hasimplications for the interpretation of frequency data even where no knowledge is availableto aid the process. According to the probabilistic account of cause, the appropriate strategyfor interpreting a probability distribution is to assess the difference between the twoconditional probabilities, p(BA) and p (B¬ A), where A is the putative cause and B is theeffect. If the distribution is in the form of a 23 2 table of frequencies, then the data in eachcell have to be taken into account to compute these conditional probabilities. Naive indi-viduals sometimes carry out this strategy (Lober & Shanks, 1999), but often they fail to doso (Beyth-Marom, 1982; Mandel & Lehman, 1998). Some theorists have defended the failureas adaptive (cf. Anderson & Sheu, 1995; Gigerenzer & Hoffrage, 1995; 1999), but Over &Green (2001) argue convincingly that the correct Bayesian response must take into accountall four cells in the table. However, if causation has the meaning shown in Table 2, then itis not necessary to take into account all four frequencies in order to establish a causalrelation. Indeed, what matters is not how often something occurs, but whether or not it occurs(see Schwartz et al., 1998).

Suppose you want to test whether or not a set of observations supports the followingcausal relation: Heating water to 100 °C in normal air pressure causes it to boil. If youobserve cases of boiling water at 100 °C, and no cases of water at 100 °C failing to boil, thenyou are almost there. It suffices to establish, if you don’t already know, that water is not


invariably boiling. The frequencies of the various observations do not matter. Whether or notwater boils at another temperature is not strictly relevant to the causal claim. If it doesn’t,then heating it to 100 °C is the unique cause of boiling; if it does, then heating it to 100 °Cis merely one cause of boiling. In more abstract terms, a causal relation of the formA causesB, can be inferred from the occurrence of cases of A and B, and the absence of cases of Aand not-B, granted that B is not invariable. Thementalmodels of the relation make explicit,however, only the conjunction of A and B. Hence, the theory predicts that there should bea bias towards this contingency in assessments of causation. Such a bias occurs, particularlyin situations in which there is more than one putative cause (Schustack & Sternberg, 1981).Otherwise, individuals do tend to take into account cases of A and not-B (Einhorn &Hogarth, 1978). With binary variables in the form of “present” versus “absent,” they arelikely to focus on the co-occurrence of the cause and effect. But, if both values of a variablehave to be represented in models, for example, “high” versus “low,” then participants aremore likely to take into account falsifying cases (Beyth-Marom, 1982).

When cases of A and not-Bdo occur, there are two possibilities: either A does not causeB, or A may have occurred in the absence of an enabling condition –or, equivalently, in thepresence of a disabling condition. It becomes necessary to make observations of theco-occurrence of potential enablers and disablers, and the circumstances may be as complexas those that we spelled out for Experiment 2. It is not easy to determine the correct relations.An effect may have multiple alternative causes; it may have multiple enabling conditions(Hart & Honore, 1959, 1985). Where there are competing causes, as the model theorypredicts, people tend to focus on a single cause and to discount other potential causes(Shaklee & Fischhoff, 1982), just as they focus on single options in decision making(Legrenzi et al., 1993) and single explanations in induction (Sloman, 1994).

6. Conclusion

Our results substantiate the model theory of causal relations. The theory is founded on afew simple, but powerful, principles. The meanings of causal relations are sets of possibil-ities in which an effect cannot precede a cause. Naive individuals can envisage thesepossibilities in fully explicit models, but with complex descriptions they tend to rely onmental models representing only what is true in the possibilities. They deduce the conse-quences of causal claims from what holds in their mental models of the premises. Deductionsthat they cannot make in this way are likely to be beyond them.

Acknowledgments

We thank Paolo Legrenzi and Maria Sonino Legrenzi for carrying out Experiment 3,Riccardo Varaldo, Director of the Scuola Superiore Sant’Anna of Pisa, for allowing us to testapplicants to the school, and Stefania Pizzini for help in analyzing the results. We thank RuthByrne, Denise Cummins, Jonathan Evans, Vittorio Girotto, James Greeno, Daniel Schwartz,Steve Sloman, and Paul Thagard, for their constructive comments on an earlier version of


this paper. We are grateful to many colleagues for their help: Patricia Barres, Victoria Bell,Zachary Estes, David Green, Denis Hilton, Patrick Lemaire, Bradley Monton, HansjoergNeth, Mary Newsome, David Over, Sergio Moreno Rios, David Shanks, Larry Solan,Vladimir Sloutsky, Jean-Baptiste van der Henst, and Yingrui Yang. Part of the research waspresented to the Workshop on Deductive Reasoning at London Guildhall University inJanuary 1999, and the authors are grateful to its organizer, David Hardman, and theparticipants for their advice. The research was supported in part by NSF Grant 0076287.

References

Ahn, W., & Bailenson, J. (1996). Causal attribution as a search for underlying mechanism: an explanation of theconjunction fallacy and the discounting principle.Cognitive Psychology, 31,82–123.

Ahn, W., Kalish, C. W., Medin, D. L., & Gelman, S. A. (1995). The role of covariation versus mechanisminformation in causal attribution.Cognition, 54,299–352.

Anderson, J. R., & Sheu, C-F. (1995). Causal inferences as perceptual judgments.Memory & Cognition, 23,510–524.

Bell, V., & Johnson-Laird, P. N. (1998). A model theory of modal reasoning.Cognitive Science, 22,25–51.Beyth-Marom, R. (1982). Perception of correlation reexamined.Memory & Cognition, 10,511–519.Braine, M. D. S., & O’Brien, D.P. (Eds.). (1998).Mental Logic.Mahwah, NJ: Lawrence Erlbaum Associates.Bucciarelli, M., & Johnson-Laird, P. N. (1999). Strategies in syllogistic reasoning.Cognitive Science, 23,

247–303.Bullock, M., Gelman, R., & Baillargeon, R. (1982). The development of causal reasoning. In Friedman, W.J.

(Ed.) The Developmental Psychology of Time.pp. 209–254. Orlando, FL: Academic Press.Burks, A. (1951). The logic of causal propositions.Mind, LX, 363–382.Byrne, R. M. J. (1997). Cognitive processes in counterfactual thinking about what might have been. In Medin,

D.K. (Ed.) The psychology of learning and motivation: advances in research and theory,Vol. 37 (pp.105–154). San Diego, CA: Academic Press.

Byrne, R. M. J., & Johnson-Laird, P.N. (1989). Spatial reasoning.Journal of Memory and Language, 28,564–575.

Byrne, R. M. J., & Johnson-Laird, P.N. (1992). The spontaneous use of propositional connectives.QuarterlyJournal of Experimental Psychology, 45,89–110.

Carnap, R. (1966).Philosophical Foundations of Physics.New York: Basic Books.Cheng, P. W. (1997). From covariation to causation: a causal power theory.Psychological Review, 104,367–405.Cheng, P. W., Holyoak, K. J., Nisbett, R. E., & Oliver, L. M. (1986). Pragmatic versus syntactic approaches to

training deductive reasoning.Cognitive Psychology, 18,293–328.Cheng, P. W., & Nisbett, R. E. (1993). Pragmatic constraints on causal deduction. In Nisbett, R.E. (Ed.)Rules

for reasoning.(pp. 207–227). Hillsdale, NJ: Lawrence Erlbaum Associates.Cheng, P. W., & Novick, L. R. (1990). A probabilistic contrast model of causal induction.Journal of Personality

and Social Psychology, 58,545–567.Cheng, P. W., & Novick, L. R. (1991). Causes versus enabling conditions.Cognition, 40,83–120.Clark, H. H., & Clark, E. V. (1977).Psychology and language: an introduction to psycholinguistics.New York:

Harcourt Brace Jovanovich.Cummins, D. D. (1995). Naı¨ve theories and causal deduction.Memory & Cognition, 23,646–658.Cummins, D. D. (1998). The pragmatics of causal inference.Proceedings of the twentieth annual conference of

the cognitive science society(p. 9).Cummins, D. D., Lubart, T., Alksnis, O., & Rist, R. (1991). Conditional reasoning and causation.Memory and

Cognition, 19,274–282.


Einhorn, H. J., & Hogarth, R. M. (1978). Confidence in judgment: persistence of the illusion of validity.Psychological Review, 85,395–416.

Einhorn, H. J., & Hogarth, R. M. (1986). Judging probable cause.Psychological Bulletin, 99,3–19.Fisher, R. A. (1959).Smoking.London: Oliver & Boyd.Garnham, A., & Oakhill, J. V. (1996). The mental models theory of language comprehension. In Britton, B.K.,

& Graesser, A.C. (Eds.)Models of understanding text.(pp. 313–39). Hillsdale, NJ: Erlbaum.Geminiani, G. C., Carassa, A., & Bara, B. G. (1996). Causality by contact. In Oakhill, J., & Garnham, A. (Eds.)

Mental models in cognitive science.(pp. 275–303). Hove, East Sussex: Psychology Press.Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: frequency

formats.Psychological Review, 102,684–704.Gigerenzer, G., & Hoffrage, U. (1999). Overcoming difficulties in Bayesian reasoning: a reply to Lewis & Keren

(1999) and Mellers & McGraw (1999).Psychological Review, 106,425–430.Girotto, V., Legrenzi, P., & Rizzo, A. (1991). Event controllability in counterfactual thinking.Acta Psychologica,

78, 111–133.Goldvarg, Y., & Johnson-Laird, P. N. (2000). Illusions in modal reasoning.Memory & Cognition, 28,282–294.Green, D. W. (2001). Understanding microworlds.Quarterly Journal of Experimental Psychology,in press.Green, D. W., & Over, D. E. (2000). Decision theoretic effects in testing a causal conditional.Current Psychology

of Cognition, 19,51–68.Grice, H. P. (1975). Logic and conversation. In Cole, P., & Morgan, J.L. (Eds.)Syntax and semantics, Vol. 3:

speech acts.New York: Academic Press.Harre, R., & Madden, E. H. (1975).Causal powers.Oxford: Blackwell.Hart, H. L. A., & Honore, A. M. (1985).Causation in the law.(2nd ed.) Oxford: Clarendon Press. (First edition

published in 1959.).Hesslow, G. (1988). The problem of causal selection. In Hilton, D.J. (Ed.)Contemporary science and natural

explanation: commonsense conceptions of causality(pp. 11–32). Brighton, Sussex: Harvester Press.Hilton, D. J., & Erb, H-P. (1996). Mental models and causal explanation: judgements of probable cause and

explanatory relevance.Thinking & Reasoning, 2,273–308.Hume, D. (1988).An Enquiry Concerning Human Understanding.A. Flew. (Ed.) La Salle, IL: Open Court.

(Originally published 1748.)Hume, D. (1978).A Treatise on Human Nature.L.A. Selby-Bigge (2nd ed.). Second ed. Oxford: Oxford

University Press. (Originally published 1739.)Johnson-Laird, P. N. (1983).Mental models: towards a cognitive science of language, inference and conscious-

ness.Cambridge: Cambridge University Press; Cambridge, MA: Harvard University Press.Johnson-Laird, P. N., & Barres, P. E. (1994). When ‘or’ means ‘and’: a study in mental models.Proceedings of

the sixteenth annual conference of the cognitive science society,475–478.Johnson-Laird, P. N., & Byrne, R. M. J. (1991).Deduction.Hillsdale, NJ: Lawrence Erlbaum Associates.Johnson-Laird, P. N., & Byrne, R. M. J. (2001). Conditionals: a theory of their meaning, pragmatics, and role in

inference. Under submission.Johnson-Laird, P. N., Legrenzi, P., Girotto, P., & Legrenzi, M. S. (2000). Illusions in reasoning about consistency.

Science, 288,531–532.Johnson-Laird, P. N., Legrenzi, P., Girotto, P., Legrenzi, M. S., & Caverni, J-P. (1999). Naive probability: a

mental model theory of extensional reasoning.Psychological Review, 106,62–88.Johnson-Laird, P. N., & Savary, F. (1999). Illusory inferences: a novel class of erroneous deductions.Cognition,

71, 191–229.Kahneman, D., & Miller, D. T. (1986). Norm theory: comparing reality to its alternative.Psychological Review,

93, 75–88.Kahneman, D., & Tversky, A. (1982). The simulation heuristic. In Kahneman, D., Slovic, P., & Tversky, A.

(Eds.)Judgment under uncertainty: heuristics and biases.Cambridge: Cambridge University Press.Kant, I. (1934).Critique of pure reason.Translated Meiklejohn, J.M.D. New York: Dutton. (Originally published

1781.)Kelley, H. H. (1973). The processes of causal attribution.American Psychologist, 28,107–128.


Koslowski, B. (1996).Theory and evidence: the development of scientific reasoning.Cambridge, MA: MIT Press.Legrenzi, P., Girotto, V., & Johnson-Laird, P. N. (1993). Focussing in reasoning and decision making.Cognition,

49, 37–66.Legrenzi, M., Legrenzi, P., Girotto, V., & Johnson-Laird, P. N. (2001). Reasoning to consistency: a theory of

naıve nonmonotonic reasoning. Under submission.Legrenzi, P., & Sonino, M. (1994). Psychologistic aspects of Suppes’s definition of causality. In Humphreys, P.

(Ed.) Patrick Suppes: scientific philosopher, Vol, 1(pp. 381–399). The Netherlands: Kluwer.Leslie, A. M. (1984). Spatiotemporal contiguity and perception of causality in infants.Perception, 13, 287–305.Leslie, A. M. (1994). Pretending and believing: issues in the theory of ToMM [Theory of Mind Mechanism].

Cognition, 50,211–238.Lewis, C. (1986). A model of mental model construction.Proceedings of CHI ‘86 conference on human factors

in computer systems.New York: Association for Computing Machinery.Lewis, D. (1973).Counterfactuals.Oxford: Blackwell.Lober, K., & Shanks, D. R. (1999). Experimental falsification of Cheng’s (1997) Power PC theory of causal

induction.Psychological Review,in press.Lombard, L. M. (1990). Causes, enablers, and the counterfactual analysis.Philosophical Studies, 59,195–211.Mackie, J. L. (1980).The cement of the universe: a study in causation.(2nd ed.) Oxford: Oxford University Press.Mandel, D. R., & Lehman, D. R. (1998). Integration of contingency information in judgements of cause,

covariation and probability.Journal of Experimental Psychology: General, 127,269–285.Markovits, H., & Savary, F. (1992). Pragmatic schemas and the selection task: to reason or not to reason.

Quarterly Journal of Experimental Psychology,45A, 133–148.McArthur, L. (1972). The how and what of why: some determinants and consequences of causal attribution.

Journal of Personality and Social Psychology, 22,171–193.McEleney, A., & Byrne, R. M. J. (2001). Counterfactual thinking and causal explanation. Under submission.McGill, A. L. (1989). Context effects in judgments of causation.Journal of Personality and Social Psychology,

57, 189–200.Michotte, A. (1963).The perception of causality.London: Methuen. (Originally published 1946.)Mill, J.S. (1874)A system of logic, ratiocinative and inductive: being a connected view of the principles of

evidence and the methods of scientific evidence.(8th ed.) New York: Harper. (First edition published 1843.)Miller, G. A., & Johnson-Laird, P. N. (1976).Language and perception.Cambridge, MA: Harvard University

Press.Miyake, N. (1986). Constructive interaction and the iterative process of understanding.Cognitive Science, 10,

151–177.Morris, M. W., & Nisbett, R. E. (1993). Tools of the trade: deductive schemas taught in psychology and

philosophy. Nisbett, R.E. (Ed.)Rules for reasoning(pp. 228–256). Hillsdale, NJ: Lawrence ErlbaumAssociates.

Newstead, S. E., Ellis, M. C., Evans, J.St.B.T., & Dennis, I. (1997). Conditional reasoning with realistic material.Thinking & Reasoning, 3,49–76.

Osherson, D. N. (1974–6).Logical abilities in children, Vols. 1–4.Hillsdale, NJ: Lawrence Erlbaum Associates.Over, D. E., & Green, D. W. (2001). Contingency, causation, and adaptive inference.Psychological Review,in

press.Pearl, J. (1988).Probabilistic reasoning in intelligent systems: networks of plausible inference.Revised Second

Printing. San Francisco: Morgan Kaufmann.Reichenbach, H. (1956).The direction of time.Berkeley: University of California Press.Rips, L. J. (1994).The psychology of proof.Cambridge, MA: MIT Press.Russell, B. A. W. (1912–13). On the notion of cause.Proceedings of the Aristotelian Society, 13,1–26.Salmon, W. C. (1980). Probabilistic causality.Pacific Philosophical Quarterly, 61,50–74.Santamaria, C., Garcia-Madruga, J. A., & Johnson-Laird, P. N. (1998). Reasoning from double conditionals: the

effects of logical structure and believability.Thinking and Reasoning, 4,97–122.Schaeken, W. S., Johnson-Laird, P. N., & d’Ydewalle, G. (1996). Mental models and temporal reasoning.

Cognition, 60,205–234.


Schustack, M. W. (1988). Thinking about causality. In Sternberg, R.J. & Smith, E.E. (Eds.)The Psychology ofthinking (pp. 92–115). Cambridge: Cambridge University Press.

Schustack, M. W., & Sternberg, R. J. (1981). Evaluation of evidence in causal inference.Journal of ExperimentalPsychology: General, 110,101–120.

Schwartz, D. L., Goldman, S. R., Vye, N. J., Barron, B. J., & CTGV. (1998). Aligning everyday and mathematicalreasoning: the case of sampling assumptions. In Lajoie, S. (Ed.)Reflections on statistics: agendas for learning,teaching and assessment in K-12.(pp. 233–274). Mahwah, NJ: Erlbaum.

Shafer, G. (1996).The art of causal conjecture.Cambridge: MIT Press.Shaklee, H., & Fischhoff, B. (1982). Strategies of information search in causal analysis.Memory & Cognition,

10, 520–530.Shultz, T. R. (1982). Rules of causal attribution.Monographs of the Society for Research in Child Development,

47, 1–51.Sloman, S. A. (1994). When explanations compete: the role of explanatory coherence on judgments of likelihood.

Cognition, 52,1–21.Stalnaker, R. (1968). A theory of conditionals. In Rescher, N. (Ed.)Studies in logical theory.pp. 98–112. Oxford:

Blackwell.Stevenson, R. J. (1993).Language, thought and representation.New York: Wiley.Suppes, P. (1970).A probabilistic theory of causality.Amsterdam: North-Holland.Suppes, P. (1984).Probabilistic metaphysics.Oxford: Basil Blackwell.Taylor, R. (1966).Action and purpose.Englewood Cliffs, NJ: Prentice-Hall.Thompson, V. A. (1995). Conditional reasoning: the necessary and sufficient conditions.Canadian Journal of

Experimental Psychology, 49, 1–60.Tooley, M. (1987).Causality: a realist approach.Oxford: Oxford University Press.Turnbull, W., & Slugoski, B. R. (1988). Conversational and linguistic processes in causal attribution. In Hilton,

D. (Ed.)Contemporary science and natural explanation: commonsense conceptions of causality(pp. 66–93).Brighton, Sussex: Harvester Press.

Tversky, A., & Kahneman, D. (1980). Causal schemas in judgments under uncertainty. In Fishbein, M. (Ed.)Progress in social psychology.Hillsdale, NJ: Lawrence Erlbaum Associates.

Vendler, Z. (1967).Linguistics in philosophy.Ithaca, NY: Cornell University Press.von Mises, R. (1957).Probability, statistics and truth.Second revised English edition based on the third German

Edition of 1951. London: Allen & Unwin.von Wright, G. H. (1973). On the logic and epistemology of the causal relation. In Suppes, P. (Ed.)Logic,

methodology and philosophy of science, IV(pp. 293–312). Amsterdam: North-Holland.Wason, P. C. (1966). Reasoning. In Foss, B.M. (Ed.)New horizons in psychology.Harmondsworth, Middlesex:

Penguin.White, P. A. (1995). Use of prior beliefs in the assignment of causal roles: causal powers versus regularity-based

accounts.Memory and Cognition, 23,243–254.Yang, Y., & Johnson-Laird, P. N. (2000). Illusions in quantified reasoning: how to make the impossible seem

possible, andvice versa. Memory & Cognition, 28,452–465.


naive causality: a mental model theory of causal …modeltheory.org/papers/2001causality.pdfnaive...

Documents